WASHINGTON — President Biden promised Americans he is making 500 million coronavirus tests available free of charge, but help is at least weeks away — if not longer — for anxious Americans facing a surge of new virus cases.

Mr. Biden’s administration has not yet signed a contract to buy the tests, and the website to order them will not be up until January. Officials have not said how many tests people will be able to order or how quickly they will be shipped once they begin to be available next month. Manufacturers say they are already producing tests as fast as they can.

As a candidate, Mr. Biden excoriated the lack of testing during the Trump administration, saying in March 2020 that “the administration’s failure on testing is colossal, and it’s a failure of planning, leadership and execution.” But the Omicron variant caught the White House off guard, as the president has acknowledged, and cases have far outstripped the government’s ability to make tests available.

The president’s pledge of a half-billion tests on Tuesday was the centerpiece of a newly aggressive testing effort, announced just days before Christmas, as Americans try to find the hard-to-find tests so they know whether they are infected during the holiday season.

“That’s not a plan — it’s a hope,” said Jennifer Nuzzo, an epidemiologist at the Johns Hopkins Bloomberg School of Public Health, which tracks testing trends. “If those tests came in January and February, that could have an impact, but if they are spread out over 10 to 12 months, I’m not sure what kind of impact it is going to have.”

Contracts to purchase tests could be finalized as soon as next week, officials said.

Whether testing manufacturers can now ramp up to produce an extra 500 million at-home tests — and how soon — is unclear. John M. Koval, a spokesman for Abbott Laboratories, a major manufacturer of rapid at-home antigen tests, said in an email message that the company is seeing “unprecedented demand” for its tests, “and we’re sending them out as fast as we can make them.”

The company is running its manufacturing plants around the clock, investing in automation and hiring more workers, Mr. Koval said. Abbott will make 70 million tests in January, he said, and “can scale significantly in the months ahead.”

Ellume, an Australian manufacturer of a competing rapid test, said in a statement that it “stands ready to meet the increased demand” by supplying the government 8.5 million tests, and opening a new manufacturing facility in Frederick, Md., in January. Once fully operational, that plant will produce 15 million tests a month.

The Biden plan is facing competition from state and local officials who got out ahead of the president. In Maryland, Gov. Larry Hogan announced last month that his administration was making 500,000 Abbott at-home tests available. Colorado began distributing free at-home tests in October. Dozens of cities and towns in Massachusetts are already sending out free tests under a new statewide program.

Experts say it is unlikely that the 500 million new tests will become available all at once. Dr. Michael Mina, an epidemiologist and former Harvard professor who has repeatedly called for expanded use of testing, said he expected that they would be distributed over two to three months.

“Had this been started a long time ago, maybe things would be a bit different,” said Dr. Mina, who recently became the chief science officer of eMed, which distributes at-home tests. “But this is where we are now, and we kind of have to deal with it.”

Shortages of at-home tests are not unique to the United States. In the last week, headlines have blared about long lines for testing in Spain, Britain, Canada, Germany and Ireland.

The White House also noted that the government has increased other methods of testing over the past several months, including sending 50 million free tests to community health centers and surging help to hot spots.

By next week, a team from the Centers for Disease Control and Prevention will be in New York City helping to provide an additional 25,000 of the more sensitive laboratory-conducted tests. The first mobile site opened in Queens on Wednesday, and two more will open Thursday in Flushing and East Elmhurst, New York officials said.

Jen Psaki, the White House press secretary, said Wednesday that the 500 million tests are “the biggest purchase that we have done to date.”

“It certainly represents a significant commitment, a recognition by the president that we need to be doing more,” she said.

For Mr. Biden, the scramble to address the shortfall in the availability of testing is an uncomfortable parallel with the Trump administration’s inability to roll out testing at the beginning of the pandemic in 2020.

The Trump administration struggled with supply shortages and a president who complained that testing was driving up caseload reports and making him look bad.

Mr. Biden came into office vowing to expand the supply of tests but later focused his response almost exclusively on vaccines, and demand for testing fell so low that Abbott destroyed millions of tests in August — just as the Delta variant was surging.

The lack of tests at the beginning of the pandemic blinded the government to the virus’s early spread, a failure that contributed to the high toll in lives in the first wave of infection. At the time, Mr. Biden pledged that as president he would form a pandemic testing board — a play on Franklin Delano Roosevelt’s War Production Board — and vastly increase testing.

“Testing unequivocally saves lives, and widespread testing is the key to opening up our economy again,” Mr. Biden said in June 2020.

Mr. Biden’s administration followed through on those promises early in his term, helping states set up a network of drive-through testing sites working to spur development of rapid, in-home tests. He did create a testing board, White House officials said, which is composed of officials from various government agencies. The Food and Drug Administration accelerated the pace of approving at-home tests; now there are about a dozen available, up from none when he took office.

But the drive-in sites largely closed in the summer amid slumping demand as the pace of vaccinations picked up and caseloads dropped. At that time, the C.D.C. told vaccinated Americans they did not need to test if they were exposed to the coronavirus but had no symptoms. The agency reversed that guidance in September.

The United States was performing an average of 1.8 million tests per day at its peak in January, according to the Johns Hopkins data, but by July of this year, that had dropped to 424,000, even as the Delta variant began to emerge. (Today’s average stand at 1.57 million tests per day.)

The destruction of Abbott’s tests in August came precisely as the administration should have been preparing for a fall and winter surge, said Dr. Nuzzo of Johns Hopkins.

“There was no forward-looking, ‘Well, what if cases go up again? How will be build back the infrastructure that we let erode?’” she said, adding, “It was a pretty reasonable expectation that cases could go up again.”

After Omicron hit at the end of November, the president announced that those with private insurance could be reimbursed for the purchase of at-home tests, and pledged to deliver 50 million rapid tests to community health centers.

The testing announcement on Tuesday, which expanded on that commitment, reflected how the Omicron surge caught the White House off guard — as Mr. Biden himself acknowledged when reporters questioned him at the White House.

“What happened was the Omicron virus spread even more rapidly than anybody thought,” Mr. Biden said. “If I told you four weeks ago that this would spread, on a day-to-day basis, it would spread by 50 percent, 100 percent, 200 percent, I think you would have looked at me and said, ‘Biden, what are you drinking?’”