Ms. Bennett was leading her closest primary opponent, Tina Shah, by roughly 27 percentage points when The Associated Press called the race in her favor an hour after polls closed.

She thanked her supporters gathered in Bridgewater, N.J., in a rousing address.

“If this group of badass American patriots can get a political outsider — a 2010 Honda Accord-driving, Navy-veteran mom — to win in one of the most competitive primaries in the country, we are going to flip this seat,” Ms. Bennett said.

“Hard does not scare me,” she said, adding: “We cannot just be anti-Trump and anti hate. We have to be for something. We have to solve the problems that we are all facing in our everyday lives.”

Mr. Kean, 57, had no challenger in Tuesday’s Republican primary. But intrigue over an unexplained health condition that has caused him to vanish from public life since the middle of March has overshadowed much of the debate in recent months. He has missed more than 100 votes during his absence, at a time when Republicans hold a narrow House majority and are working to advance the president’s agenda ahead of the midterm elections.

“Where is Congressman Kean?” an editorial in the Leader, the local newspaper in Westfield, N.J., where Mr. Kean has lived for decades, asked on Thursday.

Ms. Bennett’s military background has led to comparisons with New Jersey’s governor, Mikie Sherrill, a Democrat who also flew helicopters in the Navy. Ms. Sherrill cruised to a 14-point victory last year against her Republican opponent, Jack Ciattarelli, outperforming most pre-election polls.

Ms. Bennett, 39, has emphasized her military service, her role as a mother and her willingness to take on Mr. Trump, much like Ms. Sherrill did in her campaign for governor. Ms. Bennett’s campaign website features a photo of her in front of a gunmetal gray helicopter, wearing a wide grin and a pilot’s jumpsuit as she holds her newborn daughter.

Pat Ick, a Democrat who cast a ballot on Sunday during New Jersey’s six-day early voting period, said Ms. Bennett’s military service was a deciding factor.

“She’s a fighter,” said Ms. Ick, of Westfield. “She’ll fight for this country.”

Ms. Bennett had a more than two-to-one lead over Dr. Shah, a physician, with about 75 percent of the vote tallied. Brian Varela, who owns a network of child care centers, and Michael Roth, who led the Small Business Administration during the Biden administration, were close behind Dr. Shah.

The Seventh District is expected to be a key battleground in November.

The seat has flipped between Republicans and Democrats twice in the past decade. Mr. Kean ousted a Democrat, Tom Malinowski, to win the seat in 2022. Four years earlier, Mr. Malinowski had beaten Leonard Lance, a long-serving Republican.

The district was redrawn after the 2020 census to include more Republican-leaning towns, giving Mr. Kean a mathematical edge. He also has a big head-start on fund-raising, with about $3.4 million on hand.

But his lengthy absence from Congress and from the campaign trail could prove detrimental.

“I think maybe the damage is done for him,” said Bill Morrissey, a Republican who also lives in Westfield. Mr. Morrissey, 75, voted Tuesday for Mr. Kean. But he said Ms. Bennett was also appealing.

Mr. Kean, who cast a ballot last week by mail, did not re-emerge in person on Primary Day. But his office did release a statement in which he vowed to eventually be “completely transparent” about his health condition.

“I look forward to sharing my experience with the public,” he said, adding that he was “optimistic about the road ahead.”

But Mr. Kean also seemed to suggest that it could be several more weeks before he returned to public life.

“Right now I am focused on my recovery,” he said, “and under the advice of health care professionals I will transition from virtual work to in-person work within a matter of weeks.”

An independent poll by StimSight Research suggested that the No. 1 issue for voters in Tuesday’s Democratic primary was selecting the candidate best positioned to flip the seat from red to blue to blunt Mr. Trump’s power in Washington.

Deborah Enix-Ross, a lawyer and a past president of the American Bar Association, said choosing a Democrat likely to appeal to independent voters was her foremost concern as she cast a ballot on Sunday. (The district includes 213,297 voters who are not registered with either party — only about 4,000 fewer than the number of registered Republicans.)

“Do I have to love everything about a candidate? ‘No,’ ” Ms. Enix-Ross said outside a polling location in Union County, N.J. “I’m thinking long term.”

Ms. Bennett, who until 2016 was a registered Republican, spent 13 years in the Navy and was seen as the most moderate of the four Democratic candidates. She led the primary field in fund-raising, but as the general election gets underway she has far less left to spend than Mr. Kean: about $760,000, according to her most recent campaign filing.

Spending by outside interest groups is expected to be brisk.

Last month, a new political action committee with ties to Republicans began running negative ads that sought to undermine Ms. Bennett while elevating her opponents, who were considered less likely to beat Mr. Kean in a head-to-head matchup. The PAC, Real Change, was formed last month in Nebraska and spent roughly $650,000 to discredit Ms. Bennett.

It’s a strategy that was also used in other competitive primary races across the country as the parties have jockeyed for every competitive advantage in the race for control of the House.

Ms. Sherrill, in response to the ads, scolded Republicans. “Stay out of Democratic primaries,” she said in a statement.

Ms. Bennett filed a cease-and-desist order against the PAC and responded with an ad of her own.

“I want to congratulate the Republican Party for lighting $650,000 on fire over the last two weeks,” Ms. Bennett said Tuesday night about the PAC spending. “Because you know what that tells us? They know that I am our best shot at flipping this seat in November.”