Vivek Ramaswamy, the Republican wunderkind running for his party’s presidential nomination, would like potential supporters to know he believes in the rule of law and the Constitution’s separation of powers — though his applications of such principles can seem selective.

After intense study of the Constitution, Mr. Ramaswamy says he believes that the awesome powers of the presidency would allow him to abolish the Education Department “on Day 1,” part of an assault on the “administrative state” that his 2024 rival, Donald J. Trump, fell short on during Days 1 through 1,461 of his presidency. Never mind that the Constitution confers the power of the purse on Congress, and a subsequent law makes it illegal for the president not to spend that money.

Mr. Ramaswamy also wants to eradicate teachers’ unions, though he concedes that they are governed by contracts with state and local governments.

And he says he would unleash the military to stamp out the scourge of fentanyl coming across the Southern border, unworried by the Posse Comitatus Act of 1878, which prohibits the use of the military for civil law enforcement.

In short, Mr. Ramaswamy, a lavishly wealthy 37-year-old entrepreneur and author pitching himself as a new face of intellectual conservatism, is promising to go farther down the road of ruling by fiat than Mr. Trump would or could.

“I respect what Donald Trump did, I do, with the America First agenda, but I think he went as far as he was going to go,” Mr. Ramaswamy told a crowd of about 100 on Tuesday night at Murphy’s Tap Room in Bedford, N.H. “I’m in this race to take the America First agenda far further than Donald Trump ever did.”

Mr. Ramaswamy, a Cincinnati-born son of Indian immigrants, would seem to be the longest of long shots: He has never held elective office and has vanishingly low name recognition. But he is playing to sizable crowds and exudes a confidence that can be infectious. He has already lent his well-appointed campaign more than $10 million and has said he will spend over $100 million if necessary. Recent polling, both nationally and in New Hampshire, shows him on the rise in the Republican field, though at no more than 5 percent.

His overt shots at Gov. Ron DeSantis of Florida, whom he labels a visionless “implementer” without the courage to venture into the hostile territories of college campuses or NBC News, are intended to clear what he sees as an eventual showdown with Mr. Trump. His brashest criticism of the former president is over Mr. Trump’s suggestion that he might skip primary debates, depriving Mr. Ramaswamy of the stage he says he needs to catch his rival.

Mr. Ramaswamy sees a simple path to the White House: score respectably in the Iowa caucuses, win New Hampshire, vault to the nomination — and then triumph in a landslide that would exceed Ronald Reagan’s victory over Jimmy Carter in 1980.

“Even as a freshman, he had a similar voice, confident, articulate, very sure of himself,” said Anson Frericks, a high school friend of Mr. Ramaswamy’s and a business partner at the asset management firm they founded to give investors financial options untethered to socially conscious corporations. “Confidence builds with success. It’s a virtuous cycle.”

And though his promises may be legally problematic, they sound correct to many Republicans — or at least authoritative.

“He seems like he knows what he’s talking about,” said Bob Willis, a self-described “Ultra-MAGA Trump person” who was waiting for Mr. Ramaswamy to arrive on Wednesday in Keene, N.H.

Confidence is Mr. Ramaswamy’s gift. His father, an engineer and a patent lawyer at General Electric, is, the candidate says, far more liberal than his son. His mother is a physician. He attributes his strict vegetarianism to his Indian roots.

A piano teacher began Mr. Ramaswamy’s political journey with long asides on the evils of government and the wrongs of Hillary Clinton. At Harvard, he majored in biology and developed a brash libertarianism complete with a political rapper alter ego, “Da Vek.”

Between graduation and Yale Law School, he worked in finance, investing in pharmaceutical and biotech companies. Before getting his law degree, he was already worth around $15 million, he said in an interview, during which he worried about wealth inequality.

“I think it fuels a social hierarchy in our country that rejects the premise that we’re all coequal citizens,” he said.

Indeed, Mr. Ramaswamy’s promises have an overarching theme that the nation — especially his generation and younger — has lost its spiritual center, creating what the mathematician Blaise Pascal called “a God-shaped vacuum in the heart.” That hole is being filled, Mr. Ramaswamy says, by “secular cults” — racial “wokeism,” sexual and gender fluidity, and the “climate cult” — which can be “diluted to oblivion” only with the rediscovery of the American ideals of patriotism, meritocracy and sacrifice.

Mr. Ramaswamy can say things that stretch credulity or undermine his seriousness. He boasts on the campaign trail of his recent star turn jousting with Don Lemon just before Mr. Lemon was fired by CNN. But his statement in that exchange that Black Americans did not secure their civil rights until they secured their right to bear arms made little historical sense, since the civil rights movement was predicated on nonviolence. Indeed, the arming of the Black Panthers led to a deadly government crackdown.

Mr. Ramaswamy accepts the established science that the burning of fossil fuels is warming the planet, but his answer is to “drill, frack, burn coal” and use more fossil fuels. That will supposedly unleash economic growth that will pay for mitigation efforts to shield everyone from climate change.

He also says he is the first presidential candidate to promise to end race-based affirmative action, ignoring that this was the centerpiece of Ben Carson’s presidential run in 2016. Mr. Ramaswamy would end affirmative action by executive order, he says.

He would not spend another dollar on aid to Ukraine but would use military force to “annihilate” Mexican drug cartels.

On Wednesday night in Windham, N.H., Mr. Ramaswamy suggested he would name Robert F. Kennedy Jr., the Democratic vaccine skeptic challenging President Biden, as his running mate. On Tuesday in Bedford, he was asked by a woman with a Black son-in-law and a mixed-race grandson to clarify the meaning of “anti-woke.”

Mr. Ramaswamy — the author of “Woke Inc.: Inside Corporate America’s Social Justice Scam” — answered, “I’ve never used that word to actually describe myself,” as aides handed out stickers reading: “Stop Wokeism. Vote Vivek.”

All of this can be somewhat mystifying to prominent people who worked with him. Mr. Ramaswamy’s real fortune comes from the pharmaceutical investment and drug development firm Roivant Sciences, founded after the entrepreneur had a “brilliant” idea, said Donald M. Berwick, a former administrator of the Centers for Medicare and Medicaid Services under President Barack Obama.

Pharmaceutical giants often abandon research efforts after concluding that even if they are successful, the medicinal product might not be profitable. Roivant would then pick up such ventures and bring them to market. Roivant’s advisory board eventually included Tom Daschle, the former Democratic senator and Senate majority leader; Dr. Berwick; and Kathleen Sebelius, a health and human services secretary in the Obama administration.

Part of the appeal, Mr. Daschle said, was Mr. Ramaswamy’s commitment to bringing prescription drugs to market at affordable prices.

“I just assumed that because he was so interested in doing as much as he was to lower costs, social responsibility and corporate responsibility was part of his thinking,” Mr. Daschle said.

Then, after George Floyd’s murder in 2020, Mr. Ramaswamy began publicly castigating corporations for speaking out on social issues like Black Lives Matter, voting rights and “E.S.G.” — environmental, social and governance investing. Opinion columns in The Wall Street Journal were followed by appearances on Tucker Carlson’s now-canceled Fox News show.

“I was rather shocked,” said Dr. Berwick, who resigned from Roivant on Jan. 12, 2021. Within days, Mr. Daschle and Ms. Sebelius quit. Mr. Ramaswamy soon followed, to write three books, help start the asset management company with Mr. Frericks and run for president.

At this very early stage of the campaign, Mr. Ramaswamy is open about the limits of his appeal. Evangelical Christians who dominate the Republican caucuses in Iowa will need to be brought along to his Hindu faith. His “war with Mexico” may go over well in South Carolina, but faces resistance among more libertarian voters in New Hampshire, he said.

And New Hampshire cynics don’t quite know how seriously to take him. Victoria Gulla, 50, of Spofford, N.H., questioned whether he was part of a back-room deal with Mr. Trump to help take out Mr. DeSantis in exchange for a position in the next Trump administration, in the way she thinks Chris Christie, the former New Jersey governor, helped take down Senator Marco Rubio in New Hampshire in 2016.

In a statement on Friday afternoon, Mr. Trump fueled that kind of speculation, saying he was “pleased to see that Vivek Ramaswamy is doing so well” in a recent poll and “seems to be on his way to catching Ron DeSanctimonious.”

A hundred million dollars in self-funding could keep Mr. Ramaswamy in the race for a long time, and some voters were clearly persuaded by Mr. Ramaswamy’s nearly messianic appeal for a spiritual and social renewal.

Gregg Dumont, 45, of Manchester, broke into tears in Windham as he praised the candidate for daring to save his children from moral decay and what he called the “racism” of identity politics.

Mr. Dumont, wearing a T-shirt picturing Mr. Trump in jail as a political prisoner, said Mr. Ramaswamy had his vote over the man on his shirt: “All the policies with an upgrade, and none of the personality,” he said. “I’m sick of the narcissism.”