The Winter Olympics are three weeks away, but tickets have yet to go on sale. Airlines are shifting schedules, creating travel confusion. Now, a spate of coronavirus outbreaks around China — including some locally transmitted cases of the fast-spreading Omicron variant — is adding to the uncertainty ahead of the Games in Beijing.

As of Wednesday, more than 20 million people remained confined to their homes in at least five cities around China. Especially worrying for officials has been a recent flare-up in Tianjin, a port city just 70 miles from Beijing that Chinese state media have previously likened to a “moat” protecting the country’s capital.

Officials have yet to determine the source of the Tianjin outbreak that infected 137 people, including at least two with the Omicron variant. One local health official said that the virus appeared to have been spreading in the community “for some time.” On Wednesday, officials in Tianjin ordered a second round of mass testing of all 14 million residents.

The surge in infections even before the arrival of thousands of athletes, journalists and officials underscores the challenge Chinese organizers face in trying to hold the Games while sticking to Beijing’s “zero Covid” standards. The country is one of the few left in the world that chases the elimination of the virus, despite the harsh measures needed and the cost imposed on the economy and people’s lives.

Even before Omicron emerged, Beijing’s Games were never going to be a typical affair. The health protocols organizers laid out in the fall had already made it clear that the Games, which are scheduled to begin on Feb. 4, would be the most extraordinarily restricted large-scale sporting event since the start of the pandemic.

People who are unvaccinated will have to spend their first 21 days in Beijing in solitary quarantine. Fully vaccinated participants will be required to remain in a tightly managed “closed-loop” bubble from the moment they arrive in Beijing to the time they leave. They also must present two negative tests before arrival, take tests daily and submit health reports to the authorities using a mobile app.

Despite the recent outbreaks, the organizers appear determined to deliver the “green, safe and simple” Games that China’s authoritarian leader, Xi Jinping, called for last week. Officials said the authorities so far had no plans to lock down Beijing, or to change either the Olympics schedule or virus-control measures in response to Omicron.

“Whatever difficulties and challenges we may encounter, our determination to host a successful Games as planned remains firm and unwavering,” Zhao Weidong, the organizing committee spokesman, said on Tuesday.

But some basic questions remain, including how to allow fans to attend. Officials have said only residents of mainland China would be allowed as spectators, and that they should only clap — not cheer.

At the Tokyo Games last summer, more than 400 infections were recorded in the bubble; China is going to great lengths to limit the risk of an outbreak. Anyone in the bubble who tests positive must stay in a high-security government hospital or quarantine facility until two lab tests — also known as P.C.R. tests — at least 24 hours apart find no more trace of the virus, which can take weeks.

Officials also acknowledged concerns among residents that infections could occur within the bubble and then spread outside. On Sunday, Beijing traffic authorities urged residents to stay away from any collisions involving vehicles from the closed-loop bubble, saying that a special unit of ambulances would respond to such accidents.

For the Chinese government, a lot is at stake. Beijing’s zero-tolerance approach relies on mass testing, stringent border controls, expansive surveillance, contact tracing, extensive quarantines and lockdowns to tame sporadic outbreaks.

That strategy has drawn criticism at times, as in the city of Xi’an last month, when residents complained of food shortages and being denied urgent medical care. But it retains widespread public support. And Beijing has used its success to assert the superiority of its top-down authoritarian system compared with Western democracies, which have struggled to contain outbreaks.

This month, China ordered the cancellation of more than two dozen scheduled flights from the United States after several passengers tested positive for the coronavirus after arriving in China. The government also recently stepped up its already onerous restrictions for inbound travelers. Starting on Thursday, travelers coming from the United States, for example, will be required to present at least two negative tests and monitor their health for seven days in their departure city before flying to China.

Yanzhong Huang, director of the Center for Global Health Studies at Seton Hall University, said that for Beijing, the Olympics were an opportunity not only to showcase China’s athletic achievements but also to validate its “zero Covid” approach to the virus.

“If they can pull this off without causing any major outbreaks, it would be another gold medal that China would be happy to claim,” Mr. Huang said.

Getting back to zero local transmissions before the Olympics may be hard. On Monday, Anyang, a city of five million in China’s central Henan Province, was locked down after recording 58 cases. At least two Omicron cases were traced to a student who had traveled from Tianjin on Dec. 28, suggesting that the variant had already been circulating in the two cities for nearly two weeks.

And the source of some of the recent outbreaks remains unclear. In Shenzhen, officials blamed contaminated packaging of imported products for a recent spread of the Delta variant, prompting city authorities on Monday to warn residents not to buy goods from high-risk countries. (Studies show that transmission of the virus from packaging is extremely rare.)

Recognizing the challenge, some Chinese health experts have recently backed away from emphasizing the “zero Covid” goal.

“Right now we don’t yet have the ability to ensure that there are zero local cases,” said Liang Wannian, a senior official of China’s National Health Commission, according to state media reports. “But we do have the ability and the confidence to quickly extinguish local cases when we find them.”

Even with China’s formidable contact-tracing capacity and high vaccination rates, Omicron could prove especially elusive, given the short window in which positive cases can be detected. Studies have also suggested that the two major Chinese vaccines, made by Sinovac and Sinopharm, are not as effective in preventing infection of the Omicron variant. (Chinese authorities have so far approved only Chinese vaccines.)

With the Olympics on the horizon, the Beijing government has urged people to refrain from unnecessary travel to the capital. The city’s health authorities are also asking residents to report themselves to the authorities if they have been to any areas recently affected by outbreaks. This week, Beijing was also one of several Chinese cities where officials said residents should stay put during the coming Lunar New Year holiday, typically the busiest travel week of the year.

“Zero Covid is becoming more and more difficult for the Chinese authorities to achieve, but it’s still achievable,” said Jin Dongyan, a virologist at the University of Hong Kong. “It just comes with a high price — to people’s everyday life and to the economy.”

Games organizers are hoping that technology might help to minimize human interaction. They have tested robots that brew coffee, make deliveries and clean surfaces — R2-D2 look-alikes that spray disinfectant.

There is even Xiaobai, or “Little White,” a waist-high robot that can detect when someone is not wearing a mask and nag the rule-flouter into compliance. Equipped with six wheels and a disinfectant dispenser, Little White is ready to take on the challenge of the Games, Li Xinglong, one of its inventors, suggested in an announcement on the official Beijing Winter Olympics website.

“Little White,” Mr. Li said, “is not afraid of the cold.”

Amy Chang Chien and Li You contributed research.