For New York City’s economy, the last 12 months have amounted to one long, brutal winter. The pandemic forced the shutdown of most of the city’s businesses, wiped out hundreds of thousands of jobs and kept away tens of millions of tourists.

By many measures, the nation’s biggest city suffered the greatest losses and faces one of the longest and steepest climbs back. Shows will not return to Broadway stages until after Labor Day, and many workers will not begin commuting to the office and buying lunch at the corner deli for months, if they return at all.

But for the first time since the city went on lockdown late last March, there are palpable signs of rebirth, fueled by a growing supply of Covid-19 vaccines and an impending gusher of federal aid to City Hall, the schools, the transit system, restaurants and theaters.

Shoots of the budding optimism pop up almost daily: The Mandarin Oriental Hotel overlooking Central Park called back workers for a reopening this week. Union Square Café, a popular Manhattan restaurant that had been closed for months, is feeding diners again. Fans were in the stands again when the Yankees opened their season in the Bronx on Thursday, though limited to one-fifth of the seats.

The city’s outlook has improved as result of the latest stimulus bill, financial analysts say, which included about $6 billion in direct aid to the city government, $6.5 billion to the Metropolitan Transportation Authority and $4 billion to the city’s public schools.

“There’s a lot of cash that’s going to come in fairly quickly here,” said Mark Zandi, chief economist at Moody’s Analytics. “It’s going to provide big pops to places that have been more or less shut down.”

The federal aid will help solve some of the city’s biggest short-term problems, including huge drops in revenue from property and sales taxes and fares that the M.T.A., which runs the subway, buses and two commuter rails, is heavily dependent on.

Still, the road to full recovery will be long and steep, business leaders and analysts say.

Entire industries, including the arts, hotels and restaurants, were decimated, with thousands of businesses closing for good. Tourism, a pillar of the economy, is years away from rebounding, according to forecasts. And many companies are making at least some remote work a permanent feature, raising questions about the future of Manhattan without legions of office workers.

“The city still has a ways to go,” said Ana Champeny, director of city studies for the Citizens Budget Commission. “You’ve got to get commuters back in Midtown and downtown, the business district. You’ve got to get restaurants and theaters reopened.”

The infusion of federal aid has provided some reason for hope.

The M.T.A. has gone from threatening to sharply reduce service and lay off workers to promising to restore 24-hour subway service, which was suspended during the pandemic.

Many restaurants that struggled to survive through a monthslong ban on indoor dining can try to recoup losses and the costs of adapting to pandemic restrictions.

Senator Chuck Schumer, the Democratic majority leader from New York, said the aid that will flow to New York State and its residents from the stimulus bill, known as the American Rescue Plan, amounted to nearly $100 billion.

Mayor Bill de Blasio will lay out a plan for spending the direct aid when he presents his budget in April, said a spokeswoman, Laura Feyer. The mayor said the aid would enable the city “to finally overcome the massive revenue loss and to serve our people, keep our work force strong, bring our city back.”

The direct local aid “can put the city on solid fiscal footing,” said Ms. Champeny, though the city still faces large budget deficits in future years. “It is an incredibly generous package that will definitely start the rebuild.”

The rebuild faces formidable challenges.

The New York metropolitan area lost more than one million jobs in 2020, close to double the Los Angeles area’s loss and triple the Chicago area’s, according to the federal Bureau of Labor Statistics. (The city’s official unemployment rate rose to 12.9 percent in February, more than double the national rate, which was 6.2 percent in February and fell to 6 percent in March.)

The job losses fell harder on those who were clinging to the lower rungs of the city’s economic ladder. Low-paying jobs that cannot be done from home accounted for most of the losses, and many may not come back for years, if ever, economists said.

New York was especially vulnerable to the pandemic’s economic pummeling because of its heavy reliance on tourists and business travelers to fill hotel beds and seats in restaurants, theaters and stadiums.

The number of foreign visitors to New York is not expected to reach its 2019 level before 2025, according to the city’s tourism promotion agency.

New York’s office towers are still largely empty, and the exodus of office workers from Manhattan — many of whom are not expected to return until the last half of the year — has crippled merchants and significantly reduced the value of much of the city’s commercial real estate, which will translate into a big drop in sales and property tax revenue.

The city’s Independent Budget Office projected that the city’s recovery would remain “fragile and tentative for many more months.”

Though a snapback in hiring this year and next would replace about 400,000 of the jobs the city lost, the budget office said that by the end of 2024 New York would still not have as many jobs as it did before the pandemic started.

More than 200 of the city’s 700 hotels remain closed, leaving thousands of workers still unemployed, said Vijay Dandapani, chief executive of the Hotel Association of New York City. “My industry fell off a cliff on March 22 last year,” he said.

Many hotel operators have received no federal aid during the pandemic, and nearly half are in default on their mortgages, Mr. Dandapani said. More than 40 hotels have fallen behind on their property tax payments to the city, which could put them in “a downward spiral” that they cannot escape, he added.

But even the beleaguered hotel business is seeing glimmers of recovery. The Mandarin Oriental rehired more than 100 members of the Hotel Trades Council union for its reopening on Thursday, the hotel’s manager, Susanne Hatje, said. The Mandarin is offering discounted rates starting at $716 per night, 20 percent below prepandemic prices.

The nearby Park Hyatt also reopened on Thursday, and other hotels are expected to join the trend as tourists trickle back. During the week that ended March 20, the city’s hotels had an occupancy rate of 50.8 percent, the highest in more than a year, according to STR, an industry research firm.

Tourism may start to pick up slightly by late summer if fans return to the stands at the U.S. Open tennis tournament in Queens. And if delegates come back to Manhattan in September for the United Nations General Assembly, hotels may fill more rooms.

The city’s tourism promotion agency, NYC & Company, has forecast that the number of visitors will climb to 38 million this year, up from about 23 million in 2020, but still down about 40 percent from a record high level in 2019.

Despite the city’s precarious situation, E.J. McMahon, founder of the Empire Center, a conservative research group, said he was wary about the extraordinary amount of federal aid flowing to the region.

The pandemic’s impact on New York’s economy appears to be much deeper and longer lasting than the effects of the Sept. 11 terrorist attack two decades ago, he said. “There’s going to be a hangover from this, a significant hangover.”

Still, Mr. McMahon questioned, “What it is that government can do to actually recreate the economy?” Many of the lost jobs, such as cleaning hotel rooms and serving food, did not require much skill or extensive training, he said. “There’s a lot of potential here for problems and abuse of the money.”

But James A. Parrott, an economist at the Center for New York City Affairs at the New School, argued that the city should use some of the federal aid to retrain workers who have lost their jobs.

“Tens of thousands of jobs will permanently disappear, and the city needs to do more to preserve the businesses that are trying to hang on,” Mr. Parrott said. “The city has never had a challenge on this scale before.”

The restaurant business is one important part of New York’s private-sector economy that will benefit directly from the stimulus bill. The bill included more than $28 billion for restaurants across the nation that have been among the businesses worst hit by the pandemic’s economic fallout.

A sizable chunk of that aid will likely go to New York’s restaurants because they experienced some of the longest and most severe restrictions, said Andrew Rigie, executive director of the NYC Hospitality Alliance, a trade group. A recent survey by the Partnership for New York City, an influential business group, estimated that 5,000 restaurants in the city had shut down for good during the pandemic.

“This will save countless restaurants and jobs,” Mr. Rigie said. “It’s horrible that restaurants had to wait a year for this funding, but better late than never.”

While it may take some time, “the city is going to see a big revival,” Mr. Zandi said. “It’s going to come roaring back.”