On a snowy tarmac at Amari Air Base in northern Estonia on Sunday morning, pallets of rifles, ammunition and other weapons were being loaded onto one of the largest cargo planes in the world, an Antonov AN-124, belonging to the Ukrainian air force. It is an artifact of the Cold War, built and purchased when Ukraine was still part of the Soviet Union.

Now it is being turned back against the Russian invasion of Ukraine, part of a vast airlift that American and European officials describe as a desperate race against time, to get tons of arms into the hands of Ukrainian forces while their supply routes are still open. Scenes like this, reminiscent of the Berlin airlift — the famed race by the Western allies to keep West Berlin supplied with essentials in 1948 and 1949 as the Soviet Union sought to choke it off — are playing out across Europe.

In less than a week, the United States and NATO have pushed more than 17,000 antitank weapons, including Javelin missiles, over the borders of Poland and Romania, unloading them from giant military cargo planes so they can make the trip by land to Kyiv, the Ukrainian capital, and other major cities. So far, Russian forces have been so preoccupied in other parts of the country that they have not targeted the arms supply lines, but few think that can last.

But those are only the most visible contributions. Hidden away on bases around Eastern Europe, forces from United States Cyber Command known as “cybermission teams” are in place to interfere with Russia’s digital attacks and communications — but measuring their success rate is difficult, officials say.

In Washington and Germany, intelligence officials race to merge satellite photographs with electronic intercepts of Russian military units, strip them of hints of how they were gathered, and beam them to Ukrainian military units within an hour or two. As he tries to stay out of the hands of Russian forces in Kyiv, President Volodymyr Zelensky of Ukraine travels with encrypted communications equipment, provided by the Americans, that can put him into a secure call with President Biden. Mr. Zelensky used it Saturday night for a 35-minute call with his American counterpart on what more the U.S. can do in its effort to keep Ukraine alive without entering into direct combat on the ground, in the air or in cyberspace with Russian forces.

Mr. Zelensky welcomed the help so far, but repeated the criticism that he has made in public — that the aid was wildly insufficient to the task ahead. He asked for a no-fly zone over Ukraine, a shutdown of all Russian energy exports and a fresh supply of fighter jets.

It is a delicate balance. On Saturday, while Mr. Biden was in Wilmington, Del., his National Security Council staff spent much of the day trying to find a way for Poland to transfer to Ukraine a fleet of well-used, Soviet-made MIG-29 fighter jets that Ukrainian pilots know how to fly. But the deal is contingent on giving Poland, in return, far more capable, American-made F-16s, an operation made more complicated by the fact that many of those fighters are promised to Taiwan — where the United States has greater strategic interests.

Polish leaders have said there is no deal, and are clearly concerned about how they would provide the fighters to Ukraine and whether doing so would make them a new target of the Russians. The United States says it is open to the idea of the plane swap.

“I can’t speak to a timeline, but I can just tell you that we’re looking at it very, very actively,” Secretary of State Antony J. Blinken said on Sunday, during a trip that has taken him to Moldova, another non-NATO country that American officials fear may be next on Russian President Vladimir V. Putin’s hit list of nations to bring back into Moscow’s sphere of influence.

And in downtown Washington, lobbying groups and law firms that once charged the Ukrainian government handsomely for their services are now working for free, helping Mr. Zelensky’s embattled government plead for more sanctions on Russia.

The Ukrainians are also asking for more money for weapons, though they reject the idea that Washington is manipulating Mr. Zelensky’s image to present him as Churchill in a T-shirt, rallying his country to war. Covington & Burling, a major law firm, filed a motion pro bono on behalf of Ukraine in the International Court of Justice.

It is, in many ways, a more complex effort than the Berlin airlift three-quarters of a century ago. West Berlin was a small territory with direct air access. Ukraine is a sprawling country of 44 million from which Mr. Biden has pulled all American forces in an effort to avoid becoming a “co-combatant” in the war, a legal term that governs how far the United States can go in helping Ukraine without being considered in direct conflict with a nuclear-armed Russia.

But as the weapons flow in and if efforts to interfere in Russian communications and computer networks escalate, some U.S. national security officials say they have a foreboding that such conflict is increasingly likely. The American legal definitions of what constitutes entering the war are not Mr. Putin’s definitions, one senior American national security official warned over the weekend, speaking on the condition of anonymity because of the sensitivity of the American overt and covert efforts to aid Ukraine.

Mr. Putin warned on Saturday that any nation that attempted to impose a no-fly zone over Ukraine would be “participating in the armed conflict.” On Sunday the Russian ministry of defense issued a statement warning NATO countries like Romania against allowing their bases to be used as a safe haven for the remaining planes in the Ukrainian air force. If they do so, it said, any “subsequent use against the Russian armed forces can be regarded as the involvement of these states in an armed conflict.”

Twenty years ago this month, as American forces began to flow into Iraq, Gen. David H. Petraeus famously asked, “Tell me how this ends.” In the case of Ukraine, a senior American official said, the question resonating around the White House is more like: “Tell me how we don’t get sucked in to a superpower conflict.”

A Flow of Arms Becomes a Torrent

To understand the warp-speed nature of the arms transfers underway now, consider this: A $60 million arms package to Ukraine that the U.S. announced last August was not completed until November, the Pentagon said.

But when the president approved $350 million in military aid on Feb. 26 — nearly six times larger — 70 percent of it was delivered in five days. The speed was considered essential, officials said, because the equipment — including anti-tank weapons — had to make it through western Ukraine before Russian air and ground forces started attacking the shipments. As Russia takes more territory inside the country, it is expected to become more and more difficult to distribute weapons to Ukrainian troops.

Within 48 hours of Mr. Biden approving the transfer of weapons from U.S. military stockpiles on Feb. 26, the first shipments, largely from Germany, were arriving at airfields near Ukraine’s border, officials said.

The military was able to push those shipments forward quickly by tapping into pre-positioned military stockpiles ready to roll onto Air Force C-17 transport planes and other cargo aircraft, and flying them to about half a dozen staging bases in neighboring countries, chiefly in Poland and Romania.

Still, the resupply effort faces stiff logistical and operational challenges.

“The window for doing easy stuff to help the Ukrainians has closed,” said Maj. Gen. Michael S. Repass, a former commander of U.S. Special Operations forces in Europe.

U.S. officials say Ukrainian leaders have told them that American and other allied weaponry is making a difference on the battlefield. Ukrainian soldiers armed with shoulder-fired Javelin anti-tank missiles have several times in the past week attacked a mileslong convoy of Russian armor and supply trucks, helping stall the Russian ground advance as it bears down on Kyiv, Pentagon officials said. Some of the vehicles are being abandoned, officials said, because Russian troops fear sitting in the convoy when fuel-supply tanks are being targeted by the Ukrainians, setting off fireballs.

The convoy has also come under attack several times at different places along the column from another weapon supplied by a NATO member state. Armed Turkish Bayraktar TB2 drones, which the Ukrainian military used for the first time in combat against Russian-backed separatists in eastern Ukraine last October, are now hunting Russian tanks and other vehicles, U.S. officials said.

A senior Pentagon official, speaking on condition of anonymity to discuss operational matters, said American military officials had been impressed by how the Ukrainians had used the equipment and slowed the Russian advance.

Even the elements have sided with the Ukrainian military in the war’s early days. Bad weather in northern Ukraine has grounded some Russian attack planes and helicopters, a senior Pentagon official said. Many Russian vehicles that have driven off the main roads to avoid the stalled convoy have gotten stuck in the mud, making them more vulnerable to attack, officials said.

But the U.S. intelligence also has its limits. Mr. Biden’s ground rules forbid flying surveillance aircraft over Ukraine, so they have to peer in over the border, much as surveillance is often conducted over North Korea. There is reliance on new, small satellites — providing images similar to those that commercial firms like Maxar and Planet Labs are providing.

A War in Cyberspace That Has Barely Begun

One of the odd features of the conflict so far is that it runs the gamut of old and modern warfare. The trenches dug by Ukrainian soldiers in the south and east look like scenes from 1914. The Russian tanks rolling through the cities evoke Prague in 1956. But the battle of the present day that most strategists expected to mark the opening days of the war — over computer networks and the power grids and communications systems they control — has barely begun.

American officials say that is partly because of extensive work done to harden Ukraine’s networks after Russian attacks on its electric grid in 2015 and 2016. But experts say that cannot explain it all. Perhaps the Russians did not try very hard at the outset, or are holding their assets in reserve. Perhaps an American-led counteroffensive — part of what Gen. Paul M. Nakasone, the head of Cyber Command and the National Security Agency, calls a doctrine of “persistent engagement” in global networks — explains at least some of the absence.

Government officials are understandably tight-lipped, saying the cyberoperations underway, which have been moved in recent days from an operations center in Kyiv to one outside the country, are some of the most classified elements of the conflict. But it is clear that the cybermission teams have tracked some familiar targets, including the activities of the G.R.U., Russia’s military intelligence operations, to try to neutralize their activity. Microsoft has helped, turning out patches in hours to kill off malware it detects in unclassified systems.

All of this is new territory when it comes to the question of whether the United States is a “co-combatant.” By the American interpretation of the laws of cyberconflict, the United States can temporarily interrupt Russian capability without conducting an act of war; permanent disablement is more problematic. But as experts acknowledge, when a Russian system goes down, the Russian units don’t know whether it is temporary or permanent, or even whether the United States is responsible.

Similarly, sharing intelligence is perilous. American officials are convinced that Ukraine’s military and intelligence agencies are populated with Russian spies, so they are being careful not to distribute raw intelligence that would reveal sources. And they say they are not passing on specific intelligence that would tell Ukrainian forces how to go after specific targets. The concern is that doing so would give Russia an excuse to say it is fighting the United States or NATO, not Ukraine.

The Lobbyists Fight, Too

Ukraine has been receiving lobbying, public relations and legal assistance free of charge — and it is paying off. Mr. Zelensky held a Zoom call with members of Congress on Saturday, pushing for tougher sanctions on Russia and urging specific types of arms and other support.

An ad hoc team includes Andrew Mac, an American lawyer who has been volunteering as a lobbyist and nonstaff adviser to Mr. Zelensky since late 2019, and Daniel Vajdich, a lobbyist who had been paid by the Ukrainian energy industry and a civil society nonprofit group, but is now working for free. But American lobbyists are a sensitive topic in Ukraine, after Paul Manafort, later President Trump’s campaign chairman, worked for a pro-Russian president who was ousted in 2014, and after Mr. Trump tried to make military aid to Kyiv dependent on its willingness to help find dirt on then-candidate Biden and his son, Hunter.

Mr. Vajdich said he hoped his clients would redirect any funds they would have paid his firm to military defenses and humanitarian aid for Ukrainians forced from their homes by the fighting, drawing a comparison to early Nazi military aggression.

“Knowing what we know today, if we were living and operating in 1937 to ’39, would we have asked the Czechoslovaks for compensation to lobby against Neville Chamberlain and his policies?” he asked, referring to the British prime minister who ceded part of Czechoslovakia to Nazi Germany in the Munich Agreement of 1938.

“No,” he said, “certainly not.”

Amari Air Base,