The warnings started to stream in early this fall: Shop early or you may not get your gifts on time.

Global supply chain problems that have led to long delays in manufacturing and shipping could ripple outward, slowing package deliveries to millions of Americans in the weeks and days before Christmas, experts warned. The prospect even became a talking point in conservative attacks on President Biden’s policies.

Despite early fears, however, holiday shoppers have received their gifts mostly on time. Many consumers helped themselves by shopping early and in person. Retailers ordered merchandise ahead of time and acted to head off other bottlenecks. And delivery companies planned well, hired enough people and built enough warehouses to avoid being crushed by a deluge of packages at the last minute, as the Postal Service was last year.

The vast majority of packages delivered by UPS, FedEx and the Postal Service this holiday season are gifts destined for residential addresses, according to ShipMatrix, a software company that services the logistics industry. And nearly all have arrived on time or with minimal delays, defined as a few hours late for express packages and no more than a day late for ground shipments. The UPS and the Postal Service delivered about 99 percent of their packages on time by that measure between Nov. 14 and Dec. 11, and FedEx was close behind at 97 percent, according to ShipMatrix.

“The carriers have done their part. Consumers have done their part,” said Satish Jindel, president of ShipMatrix. “When they work together, you get good results.”

That’s not to say the supply chain turmoil is over. About a hundred container ships are waiting off the West Coast to unload their cargo. Big-ticket items, such as new cars, are still hard to find because of a shortage of some critical parts like computer chips. And prices are up for all kinds of goods.

But at least when it comes to items that are in stock, delivery companies have given consumers little to complain about. By some measures, in fact, they have done a better job this holiday season than even before the pandemic. In the two full weeks after Thanksgiving, it took about four days from the moment a package was ordered online for it to be delivered by FedEx, according to data from NielsenIQ, which tracks online transactions from millions of online shoppers in the United States. That compares with about 4.6 days for UPS and more than five days for the Postal Service.

For UPS and FedEx, those figures are an improvement of about 40 percent from a similar post-Thanksgiving period in 2019, according to NielsenIQ. For the Postal Service, it was a 26 percent improvement.

“There’s all these different moving parts that have collaborated to help us get through what might have been a perfect storm to cause problems,” Bill Seward, president of worldwide sales and solutions for UPS, said in an interview. “We feel really good about where we’re at right now.”

The achievement is all the more notable given that Americans are on track to spend more this holiday season than the one before — up to 11.5 percent over 2020, according to the National Retail Federation, a trade group.

But this year has been different in a critical way: Many people started shopping earlier.

Consumer surveys, including those commissioned by UPS and NPD Group, a market research firm, found that Americans accelerated their holiday shopping this year, motivated by shortages, shipping delays or earlier sales from retailers.

Jennifer Grisham, who lives in Southern California with her husband and three young children, was among them. Concerned by news of supply chain disruptions, Ms. Grisham asked her children to draw up their Christmas wish lists before Halloween, weeks earlier than usual. She had finished shopping by the day after Thanksgiving, which is usually when she starts buying gifts.

“I have three kids who still believe in Santa Claus,” she said. “I was not going to bookend these two really dramatic years for us with them suddenly not getting what they wanted.”

Ms. Grisham said she had little trouble finding the big-ticket items she pursued: a Barbie Dreamhouse for one daughter, Lego sets for her son and a cat condo for her other daughter, who plans to use it as a home for her stuffed animals.

“I’m happy that I got it done early, because I didn’t have to worry about the risk,” she said.

Retailers enticed consumers to shop early. Amazon and Target, for example, began holiday deals in October. According to Mr. Seward at UPS, 26 of the company’s 30 largest retail customers started offering substantial deals before Black Friday.

Many Americans also eased pressure on UPS and other delivery companies by doing more shopping in stores. After consumers switched to online shopping in droves when the pandemic took hold last year, in-store shopping bounced back strongly this year, according to retail and logistics experts. In September, in-store sales accounted for about 64 percent of retail revenue, up 12 points from its low point during the pandemic, but still somewhat below 2019 levels, according to NPD Group.

“We miss people,” Katie Thomas, a top consumer analyst at Kearney, a consulting firm, said about the compulsion to visit stores rather than buy online. “There’s a pent-up demand. We’re seeing people want to dress up again.”

Retailers and delivery companies also worked behind the scenes to make sure the supply chain disruptions did not wreak havoc on holiday packages. Retailers worked harder to forecast sales and moved inventory to areas where UPS, FedEx and others had more capacity to pick up packages. Companies that previously relied mostly or exclusively on a single delivery service started doing business with several companies.

The delivery companies have spent the past two years building out capacity, too, in response to surging demand. UPS, which in the past did not make deliveries on Saturday in much of the country, has been expanding its weekend service for years. It now offers Saturday deliveries to about 90 percent of the U.S. population. FedEx has added nearly 15 million square feet of sorting capacity to its network since June. And, starting in the spring, the Postal Service, which processes more mail and packages than the other delivery businesses, started leasing additional space and installing faster package-sorting machines around the country.

The companies have also responded by raising rates, imposing surcharges for larger packages that could slow down their networks, limiting the number of packages they will accept at busy times and penalizing retailers that ship many more or many fewer packages than they had forecast.

“We used to think that every package was the same,” Carol Tomé, UPS’s chief executive, told financial analysts in October, explaining her strategy of focusing on quality over quantity. “We don’t think that anymore. So for some shippers, we’re no longer delivering their packages, and that’s OK with us.”

The Postal Service doesn’t have the luxury of easily turning away business, but even it has done a better job of managing expectations for holiday package deliveries. Despite the introduction of its first-ever holiday surcharge last year, its delivery performance suffered. This year, however, it has fared much better, thanks to 13 million square feet of new processing space, 112 new high-speed processing machines and the decision to hire peak-season workers earlier.

“U.S.P.S. is maybe the most exciting story of all,” said Josh Taylor, senior director of professional services at Shipware, a consulting firm. “The fact that they’re not overwhelmed, that their network can continue to deliver on time, it’s a great development for consumers.”

But the holiday crunch does not end on Christmas. Online returns will keep delivery companies busy for weeks.

And the pandemic is not yet over. Fear over the spread of the Omicron variant of the coronavirus could drive consumers back to online shopping in the months to come, which would impose new pressures on delivery companies and retailers.