MANCHESTER, N.H. — A vast array of Democratic leaders, divided by generations but uniformly emboldened by President Trump’s perceived vulnerability, have begun taking palpable steps toward seeking the White House in an election that is still three and a half years away.

A prominent member of that group, former Vice President Joseph R. Biden Jr., may have sounded a starting gun for the 2020 race on Sunday night as he delivered a tough-love manifesto for the party’s future to a crowd of Democrats here.

Mr. Biden called on Democrats to deliver an optimistic message aimed at the needs of struggling Americans and to emphasize issues like health care and education, which he described as largely sidelined in the last election. “I’m absolutely positive they want to be with us,” he said of people in economic distress. “We have to prove, again, we understand that hopelessness.”

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Mr. Biden said he was prepared to storm the country to help revive the party, and boasted of his comfort in wooing areas that voted for Mr. Trump. “Wherever you want, just let me know, because it’s important,” he said.

His appearance in New Hampshire, with its crucial early primary, brought into the open some of the maneuvering among Democrats that has already gone on for months behind the scenes. The list of candidates may ultimately be the largest since 1976, when Democrats lined up after Watergate for a nomination seen as offering a short path to the White House.

In a largely leaderless party, two distinct groups are emerging, defined mostly by age and national stature. On one side are three potential candidates approaching celebrity status who would all be over 70 years old on Election Day: Mr. Biden, and Senators Elizabeth Warren of Massachusetts and Bernie Sanders of Vermont.

All three are fiery speakers inclined toward economic populism, and they have urged the Democratic Party to shift in that direction since its defeat in November.

Mr. Sanders, the runner-up in the 2016 primaries, may loom largest over the next Democratic race. He is already planning his first return trip to early-voting Iowa in July, and plans to be the keynote speaker at the convention of a social justice organization that works closely with his political group, Our Revolution.

Ms. Warren, the only one of the three who has not run for president before, has mapped out an intensive speaking schedule. Last weekend, she traveled to Detroit to address the annual fund-raising dinner for the local chapter of the N.A.A.C.P., excoriating Mr. Trump for stirring “deep ugliness” in the country. Introducing Ms. Warren was Representative Maxine Waters of California, who hailed her as a woman who “might just be the next president.”

And at a $25-per-person fund-raising event for Ms. Warren at the same venue, she was greeted with chants of “2020!” as she addressed supporters, according to Representative Debbie Dingell of Michigan.

Competing against the Democrats’ senior cohort is a large and relatively shapeless set of younger candidates who span the ideological spectrum: governors, senators, mayors, wealthy executives and even members of the House. They are animated by the president’s turbulent debut and the recent history, from Barack Obama’s victory in 2008 to Mr. Trump’s last year, of upstart candidates’ catching fire.

In the Senate alone, as much as a quarter of the Democrats’ 48-member caucus are thought to be giving at least a measure of consideration to the 2020 race, among them Cory Booker of New Jersey, Kirsten E. Gillibrand of New York, Amy Klobuchar of Minnesota and Kamala Harris of California. All are closer to 40 than 80.

Mr. Trump’s lack of conventional qualifications for the presidency may draw outside-the-box challengers who see him as having opened a range of unconventional paths.

Representative Seth Moulton of Massachusetts, a 38-year-old veteran of the Iraq war who has been a pointed critic of Mr. Trump, has not ruled out running in private conversations. High-profile city executives — like Mayor Eric Garcetti of Los Angeles, 46, and Mayor Mitch Landrieu of New Orleans, 56, who did a tour of cable shows last week after overseeing the initial removal of Confederate statues from his city — may also consider the race.

Allies of Mr. Garcetti acknowledged that national donors had broached the subject of 2020 but said that was the extent of his attention to the race. Mr. Garcetti is weighing a campaign for governor of California next year.

For now, however, it is the party’s septuagenarian trio that is casting the longest shadow over 2020, and all three have taken steps to extend or expand their leadership status in the party.

Mr. Biden’s appearance in New Hampshire was bathed in allusions to the presidency. Speaking before Mr. Biden, New Hampshire’s two senators, Jeanne Shaheen and Maggie Hassan, said they missed having him in the White House. Describing academic centers he has set up since leaving office, Mr. Biden said they housed “the people who literally would be running” the State Department under Hillary Clinton.

And he drew boos from the crowd when, in noting the news media’s attention to his speech, he seemed to joke to the press section, “Guys, I’m not running.”

The former vice president has kept intact much of his political brain trust, and he has extensive relationships in the early primary states. He and his aides have begun to map out party-building activities. He plans to address a major fund-raising event for Florida Democrats in June, and during a visit to South Carolina in April, he met with a state legislator, James Smith, to urge him to run for governor next year.

Mr. Smith, a friend of Mr. Biden’s and a supporter of his past campaigns, said he had been noncommittal about his own future.

“What the country needs is authenticity, truth, and I think he exudes that,” Mr. Smith said. “I tried to talk about his future, but he wasn’t interested in talking about his future. We talked about the future of the country, and we talked about South Carolina.”

Mr. Sanders, who is enormously popular on the left, has already begun campaigning for Democrats in the midterm elections, stumping for candidates from Nebraska to Virginia. He will go to Montana in May, before his Iowa encore.

While Mr. Sanders is mistrusted by much of the Democratic establishment, including many leading donors, he retains a huge political network, and his advisers view him as a favorite for the nomination. His decision on whether to run will shape the Democratic race, most notably for candidates like Ms. Warren, who shares much of his political base.

“If he decides to run again, he’d be an enormously formidable figure and would start as the front-runner,” said Mark Longabaugh, who helped guide Mr. Sanders’s 2016 campaign.

Mr. Longabaugh, unprompted, offered a comparison between Mr. Sanders’s grass-roots following and political infrastructure and Mr. Biden’s. “With all respect to the vice president, when you stack those assets up, I don’t even think it’s close,” he said.

In addition to her Detroit trip, Ms. Warren has used the release of her latest book, “This Fight Is Our Fight,” to travel the country in recent weeks. Betty Lu Saltzman, a pillar of Chicago’s Democratic donor community, hosted an event there for Ms. Warren, who also used the stop to meet with Mayor Rahm Emanuel, a more centrist Democrat.

This week, Ms. Warren will be the guest of honor at a fund-raising gala for Emily’s List, the Democratic women’s group, and in June, she will be the final speaker at a daylong liberal organizing meeting in San Francisco spearheaded by Susie Tompkins Buell, a prominent Democratic donor.

While some Democrats worry about running yet another candidate of Mr. Trump’s generation for president, Ms. Buell said in an interview that 2020 might be too soon for some of the party’s biggest talents — like Ms. Harris, who took office in January, and Gavin Newsom, the lieutenant governor of California, who is running for governor.

Younger Democratic hopefuls are unlikely to share Ms. Buell’s reservations. In the Senate, Mr. Booker, Ms. Gillibrand and Ms. Klobuchar have been reaching out to national donors and planning travel beyond their home states. Ms. Klobuchar is scheduled to address a Democratic Party dinner in Iowa next weekend.

Mr. Booker, who has long cultivated a donor network on the West Coast, visited Los Angeles in April to raise money and collect an award from the Humane Society. Steve Westly, a former eBay executive and major fund-raiser for the Obama and Clinton campaigns, said Mr. Booker had privately indicated that he was open to a 2020 campaign.

“He’s saying: Look, we’re all doing our best to sort out what the Trump presidency means and push back in the appropriate way,” Mr. Westly said.

Among Democratic governors, Andrew M. Cuomo of New York and Terry McAuliffe of Virginia are seen as especially active in laying groundwork for 2020. Former Gov. Martin O’Malley of Maryland, who ran in 2016, has already returned to early primary states to campaign for Democrats.

Mr. Cuomo, little seen outside New York since becoming governor in 2011, hosted a fund-raising event for the Democratic Governors Association in April, and his emissaries have approached Florida donors about a fund-raising trip this year.

Mr. McAuliffe, a former Democratic Party chairman, has reasserted himself as a political field marshal for the national party. Over the weekend, he headlined fund-raising events in Boston and New York for the National Democratic Redistricting Committee. And he has brought two trusted advisers to the organization, the former Clinton campaign officials Robby Mook and Michael Halle, who are well connected with Democrats across the country.

Democratic power brokers acknowledge that the field could grow further after the 2018 elections if a backlash against Mr. Trump brings a throng of new faces into high office.

“There’s very little downside in testing the waters and nosing around,” said Harold Ickes, a longtime Democratic strategist. “One of the lessons of 2016 is that you just don’t know. Trump is Example A of that, and Sanders is Example B.”