SACRAMENTO — Looking to jump-start his candidacy for the Democratic presidential nomination in a state where he has yet to break through, Pete Buttigieg rallied thousands Friday evening in California’s capital.

Buttigieg said the state, the biggest prize on the presidential primary calendar, would be a proving ground for his surging campaign.

“So much depends on what happens next,” said the former mayor of South Bend, Ind. “And so much depends on what happens when the future-oriented, forward-looking, racially diverse, justice-minded state of California has its say.”

The crowd cheered enthusiastically for his promise to appoint a secretary of education who valued public education and broke into a few chants of “President Pete.”

Many of those who came to the downtown Cesar Chavez Plaza, however, said they were still deciding between several candidates in a race where the top tier has yet to narrow. They said they were drawn to Buttigieg, 38, as a force for change in politics and someone who could potentially unify the country.

“It is refreshing to have a younger person go for it, rather than it just being all old men,” said Susan Nash, 18, a student from Granite Bay (Placer County) who is also considering voting for Massachusetts Sen. Elizabeth Warren. She was one of the younger members of a crowd that was largely older and white.

Buttigieg is trying to carve a moderate path to the Democratic nomination, arguing that he could win back disaffected Barack Obama voters who supported Donald Trump in 2016.

Despite top-two finishes in the early voting states of Iowa and New Hampshire, polling suggests that Buttigieg is struggling to build momentum in upcoming contests in Nevada and South Carolina, as well as key Super Tuesday states like California and Texas, where he faces a far more diverse electorate.

In California, which has already mailed out ballots for the March 3 primary, Buttigieg was in a distant fourth at the end of last month, according to the RealClearPolitics polling average. Surveys generally have shown him picking up only half the 15% support he would need to win delegates in California, though most of those polls predate the Iowa and New Hampshire voting.

Buttigieg was introduced Friday by Lt. Gov. Eleni Kounalakis, who endorsed him this week. Aside from her backing, his institutional support in the state is thin — no California members of Congress or state legislators have endorsed him.

West Sacramento Mayor Christopher Cabaldon, who interviewed Buttigieg with crowdsourced questions at Friday’s event, asked the candidate about his weakness with African Americans and other nonwhite voters. Buttigieg said they they had suffered under Trump’s presidency more than any other group and that he would appeal to them with an economic empowerment plan to close the racial wealth gap.

“The only way to win the African American vote is to deserve it,” he said.

Kim Smallwood, 50, came from San Francisco to attend the rally. She said more black voters like her would come around to Buttigieg once they found out who he was.

Smallwood was originally a Joe Biden supporter, but said she was turned off by what she felt was a weak response to Trump’s attacks on his son’s business dealings in Ukraine. She said Biden also appeared to take African Americans’ votes for granted. She said she thought Buttigieg could win by appealing to more moderate voters like her family in Missouri and help Democrats regain control of the Senate.

“The more he speaks, the more I’ve heard him say, the more I think he’s what he need,” Smallwood said.

Earlier in the day, Buttigieg held fundraisers in San Francisco and Palo Alto. The San Francisco event, a breakfast at the National LGBTQ Center for the Arts, was briefly interrupted by three protesters who were quickly ushered out, according to a pool report.

The protesters were part of an activist group of “young queer people of color” organized by the Democratic Socialists of America and San Francisco Rising Action Fund, which rallied outside the fundraiser to accuse “Wall Street Pete” of listening to wealthy donors instead of working-class voters.

A handful of LGBT protesters also appeared outside the Sacramento rally to argue that Buttigieg, who would be the first openly gay person to be elected president, isn’t liberal enough on key issues. Guillermo Riesgo, 38, a health professional from Sacramento, said Buttigieg was “co-opting the queer community for his own benefit.”

“What we need is health care,” he said. “It’s not our goal to have a president who is a member of our community.”

Alexei Koseff is a San Francisco Chronicle staff writer. Email: alexei.koseff@sfchronicle.com Twitter: @akoseff