Sen. Kirsten Gillibrand jumped into the 2020 presidential race Tuesday by announcing on “The Late Show with Stephen Colbert” that she’s forming an exploratory committee for a White House run.

“It’s an important first step and it’s one I’m taking because I’m going to run,” she said, to cheers and screams from the audience.

“I’m going to run for president of the United States because as a young mom, I’m going to fight for other people’s kids as hard as I would fight for my own, which is why I believe that health care should be a right and not a privilege.”

Gillibrand is trying to position herself as the leading woman candidate with her unabashed advocacy to boost female representation in politics while pushing issues like paid family leave.

“The way that she can stand out … is to be the woman’s advocate,” said Mona Vakilifathi, an assistant professor at NYU’s Robert Wagner Graduate School of Public Service who is teaching a policy course that studies Gillibrand. “That’s really her way in to distinguish herself. The real question is how far will that take her?”

During their conversation, Colbert pointed out to Gillibrand that campaigns operate nonstop and can take a toll on a candidate.

“You like to swear. Everyone knows that. Are you going to not swear on the campaign trail because it’s very stressful?” he asked.

“I’m going to definitely try,” Gillibrand responded.

“What’s the word you’ll miss the most?” Colbert went on.

“Um, rhymes with duck,” she responded.

“Schmuck,” came back Colbert as the audience roared.

The junior senator from New York first has to break through what will be a crowded field of Democratic competitors with bigger names.

December polling showed former Vice President Joe Biden and Sen. Bernie Sanders were early favorites in Iowa, followed by Beto O’Rourke and Sen. Elizabeth Warren.

Sens. Kamala Harris, Cory Booker, Amy Klobuchar and former New York City Mayor Michael Bloomberg formed the second tier of favorites, according to the Des Moines Register/CNN poll. Gillibrand was polling at or below 1 percent.

As No. 2 to the camera-loving Sen. Chuck Schumer and having no strong support from Gov. Andrew Cuomo, who has publicly praised Biden as the “best candidate” in the presidential field, Gillibrand will rely on her sisterhood of donors and her upstate New York roots to appeal to voters in Iowa.

“Her work as it relates to sexual harassment and the strong positions that she’s taken there and the fact that she’s from Upstate New York is going to be helpful to her as she gets out here,” said Iowa Democratic Party chairman Troy Price.

Gillibrand is expected to make upstate Troy her campaign headquarters and travel to Iowa this weekend to meet with Democratic activists.

After a record number of women ran for office in 2018 and won seats in Congress, Gillibrand’s longtime female advocacy is getting noticed.

In 2017, Gillibrand was the first Democratic senator to call for the resignation of Sen. Al Franken, who was accused of unwanted groping and kissing of women. She also made headlines when she said President Bill Clinton, a former political backer, should have resigned over the Monica Lewinsky affair. Both comments drew some rebuke from fellow Democrats for political opportunism.

But Gillibrand, a mother of two sons, said that elected leaders needed to be held to higher standards.

First elected to the House in 2006, Gillibrand was once a moderate Blue Dog Democrat who rejected amnesty for undocumented immigrants, didn’t back same-sex marriage and had a 100 percent NRA voting record.

“She’s the only person I’ve ever seen who loved guns more than any human being on Earth when she was a congresswoman from upstate New York back then,” quipped President Trump in an Oval Office interview with The Post. “She loved guns more than any person, anywhere in the United States. The day she announced she was running for the Senate. All of the sudden, ‘Gun? I’ve never heard that word before.’”

Gillibrand was appointed to the Senate in 2009 to succeed Hillary Clinton when she became secretary of state and easily won reelection to full terms in 2012 and 2018. She has moved markedly to the left in supporting gun control, same-sex marriage and calling for getting rid of ICE.

One area where she’s been a steady voice is sexual harassment. She has long pushed for reforms to end sexual assault in the military and on college campuses. And she punched back at Trump when he accused her of “begging” him for campaign donations and offering to “do anything for them.”

“You cannot silence me or the millions of women who have gotten off the sidelines to speak out about the unfitness and shame you have brought to the Oval Office,” Gillibrand replied.