Governor Hochul hopes to raise the sum for her primary campaign next year, but her recent — and unexpected — ascension has left her little time to hit that goal.Even for the governor of one of the nation’s largest states, it was a whirlwind few days. Gov. Kathy Hochul of New York greeted President Biden, bumped fists with the prime minister of Ireland, shook hands with Jay-Z and escorted British royalty though the World Trade Center site.But perhaps the highest-stakes meeting for the governor’s political future last week took place not at the United Nations General Assembly or the State Capitol, but inside an imposing limestone mansion near Central Park after business hours last Wednesday.Assembled inside were nearly two dozen of New York’s best-connected real estate developers, businessmen and lobbyists — the kind of deep-pocketed donors whose support has been crucial to winning statewide campaigns.There was John Catsimatidis, the Republican grocery store and oil refining magnate; Scott Rechler, whose company owns iconic New York skyscrapers; Alfonse M. D’Amato, a former Republican senator turned lobbyist; and Dennis Mehiel, a cardboard baron who played host for the evening.Mr. Catsimatidis described the fund-raising dinner, where Ms. Hochul raised some $200,000, as a “high-end business get-together to discuss not losing any more people from New York.”But for the new governor and the attendees paying between $10,000 and $25,000 to dine on chicken and salmon with her, the evening also represented something else: the beginning of a delicate courtship that could have huge consequences in next year’s race for governor.Barely a month after she unexpectedly ascended to the governor’s office after Andrew M. Cuomo’s resignation, Ms. Hochul is quietly revving up an aggressive fund-raising apparatus, seeking to build a formidable financial advantage — at least $10 million in donations by year’s end and as much as $25 million by next summer, donors and advisers say — to discourage or defeat potential rivals in what may be a fierce Democratic primary next year.The governor’s political ramp-up, which has involved hiring a campaign manager and other senior aides, has not gone unnoticed. Several of her potential opponents have begun more assertively positioning themselves in recent days, with their allies acknowledging that the longer they wait, the stronger Ms. Hochul may be.John Catsimatidis was among nearly two dozen wealthy donors who recently attended a fund-raising dinner for Governor Hochul.Jeenah Moon for The New York TimesJumaane D. Williams, the left-wing New York City public advocate, made the first public move on Tuesday, launching an exploratory committee. Mayor Bill de Blasio has had conversations with allies about the race; his longtime pollster recently conducted a survey aiming to assess his appeal beyond New York City, and on Tuesday, he told reporters, “I intend to stay in public service” after his second term concludes at the end of the year. Representative Thomas Suozzi, who represents parts of Long Island and Queens, has maintained an active fund-raising schedule, and his team has begun to think through who could staff a potential campaign should he decide to run.But for donors, political consultants and some of the possible candidates, the biggest open question is whether Attorney General Letitia James will enter the contest.Ms. James, who has deep ties across New York City and the potential to forge a diverse coalition, has sounded out party donors and elected officials about the race in recent weeks, leaving the impression that she is gauging possible support for a bid. Some of her allies have begun to sound increasingly confident about the likelihood of a run.And in New York City on Wednesday, Ms. James addressed a room of powerful civic, business and political leaders. She vigorously defended her investigation into Mr. Cuomo, which led to his resignation; she described her career trajectory and her own vision for the state, and, to laughter and applause, dodged a question about her political future.Ms. James has not historically had a reputation as a prolific fund-raiser. But people close to her argue that the nature of her potential candidacy — she could become America’s first Black female governor — would generate national interest, as Stacey Abrams’s run for governor of Georgia did in 2018.“It would be the first time in the history of the United States that we would have an African American woman as a governor — that I think would be very valuable in this country,” said Alan Rubin, a lobbyist in New York City who knows Ms. James and would back her if she ran. “The people who like her would support her a great deal in that effort. So I don’t think there would be difficulty in raising money.”Ms. James is raising money for her re-election as attorney general, including from wealthy donors, but she could transfer that money to another statewide account. She reported having $1.6 million in cash on hand in her most recent campaign filing in July; Ms. Hochul reported having $1.75 million in early August.Some allies of the state attorney general, Letitia James, have been bullish about her potential candidacy for governor.Dave Sanders for The New York TimesThe uncertainty of Ms. James’s status has many of the state’s most prolific donors sitting on the sidelines, or hedging bets with smaller checks while they wait to get a better sense of the field and Ms. Hochul herself. Though she was widely respected as lieutenant governor, Ms. Hochul — a ubiquitous presence at groundbreakings and ribbon cuttings for almost a decade — has only now begun to wield decision-making power in Albany, where she has won praise for taking decisive steps to implement vaccine mandates announced by her predecessor and extend the state’s eviction moratorium.“We are absolutely waiting and seeing,” said John Samuelsen, the international president of the Transport Workers Union, which gave close to half a million dollars to Mr. Cuomo’s campaigns, according to public election records, before a bitter falling out. “When we talk about Tish, we are talking about someone who has a solid record of supporting the trade workers unions and the labor movement,” he said. “Kathy Hochul has made promises that she is a true blue supporter of workers, but we will see if that’s true.”Carlo A. Scissura, the head of the New York Building Congress, said after a recent Zoom meeting with Ms. Hochul that many of the large construction and development firms his organization represents would be inclined to support her if she maintained her predecessor’s focus on large capital projects, like the Port Authority Bus Terminal and Pennsylvania Station in Manhattan and Kennedy Airport in Queens.“If the commitment to all of these things continues, then I think she’s got an opportunity to be a great governor,” he said. “If she chooses to remove projects or change projects, then people will start questioning where the priorities are.”Ms. Hochul is trying to force their hands, planning a fund-raising blitz in the weeks ahead, part of an intense schedule that has also been packed with public events.Invitations have gone out for an October event hosted by the state and city chapters of the building and construction trades councils, with a minimum donation of $5,000 from a “supporter” and $25,000 from a “friend.”Mercury Public Affairs, a lobbying and public relations firm that has a large political practice, is planning another fund-raiser for Ms. Hochul in October. Tickets start at $15,000, and organizers are hopeful it will net a total in the six figures, according to people familiar with the planning. Other fund-raisers are in the works.Earlier stops in August took Ms. Hochul to the Hamptons and Buffalo, where she lives and where there was so much interest in the run-up to her swearing-in that organizers had to turn one fund-raiser into two: an invitation-only cocktail hour honoring her birthday that cost $2,500 to attend and a larger party at a picnic ground that drew hundreds paying $50 and up.The strategy certainly carries risk. Many of her donors have pressing business before the state as she nears her first budget cycle as governor, including union contract negotiations, the fate of large capital projects initiated by Mr. Cuomo and the looming expiration of a common subsidy for housing developers.Ms. Hochul, who took office pledging to prioritize “changing the culture of Albany,” could quickly expose herself to the kind of unseemly alliances and potential conflicts that alienate many voters and some leaders of her own party.“For her to maximize her revenue as quickly as possible means she will be dealing with and talking with all kinds of people who want something from her,” said John Kaehny, the executive director of the good governance group Reinvent Albany. “That is a very slippery slope and the time pressure makes it much harder for her to manage that kind of relationship.”Meredith Kelly, a campaign adviser to Ms. Hochul, said that the governor had spent most of her first month in office focused on policy and governance related to Covid-19 and the destruction caused by the remnants of Hurricane Ida.“Of course, Governor Hochul is also setting up a strong, well-funded campaign to win in 2022, and she is grateful for the outpouring of support she has received thus far,” Ms. Kelly said.Ms. Hochul greeted Prince Harry and his wife, Meghan, at One World Observatory last week.Roy Rochlin/Getty ImagesMr. Cuomo set an extraordinary fund-raising standard for candidates running for governor, raising more than $135 million — most of it from large donors — in three campaigns. Even now, he is sitting on an $18 million war chest, according to the most recent filings, that he could deploy to meddle in the race or try to exact revenge on Ms. James for investigating his harassment and mistreatment of women, including some who worked for him.So far, Ms. Hochul appears to be emulating Mr. Cuomo’s fund-raising approach — though certainly not his domineering style — by primarily relying on donors with large checkbooks rather than the kind of grass-roots contributors who chip in $5 or $25. But her campaign has recently hired Authentic Campaigns, a consulting firm specializing in small-donor online donations that has worked for Mr. Biden and other prominent Democrats, to try to change that.“People gave Andrew money, but nobody liked him,” said Jeffrey Gural, chairman of a large real estate company who gave Mr. Cuomo more than $150,000 over the years before an acrimonious split. “You gave him money because you were afraid of him, as simple as that.”Ms. Hochul, Mr. Gural said, was much more accessible, professional and productive.He is not the only one of Mr. Cuomo’s major backers Ms. Hochul is courting. Among the guests Wednesday night at the 10,000-square-foot home of Mr. Mehiel, himself a former Cuomo donor, were a handful of the former governor’s biggest supporters, including Mr. Rechler and Lester Petracca, another real estate developer.The governor spoke in detail about reducing crime, increasing vaccination rates and restarting the city’s economy after 18 months of being rattled by the coronavirus, attendees said.She also made clear that she intended to work closely with Eric Adams, the Democratic mayoral nominee for New York City mayor who is virtually certain to win November’s general election, in what would be a major shift after years of an extraordinarily toxic relationship between Mr. Cuomo and Mr. de Blasio.Some in the crowd appeared ready for a reset.“Let’s see her actions — she deserves a break to do the right job for all New Yorkers,” said Mr. Catsimatidis, before adding a dose of Empire State realpolitik: “You know why people do fund-raisers? When they call, they want their phone calls returned.”Dana Rubinstein More