Sen. Bernie Sanders’ campaign promise to wipe out student debt for millions of Americans thrilled a packed crowd during the presidential candidate’s visit to San Francisco on Friday.

Sanders was the only major candidate for the Democratic nomination to hold a public event during the party’s three-day meeting in San Francisco this week. More than 1,000 people jammed into SVN West, a former Honda dealership on South Van Ness Avenue, where the Vermont independent rallied support for the “Pass the College for All Act” that he rolled out in June.

His message was simple.

“Financial impediments should not stop you from fulfilling your dream,” Sanders said, drawing a roar from the audience.

Sanders’ proposal would wipe out $1.6 trillion in student debt for 45 million Americans, regardless of their income status or assets. The debt-canceling initiative, along with his promise of free public higher education, would cost $2.2 trillion, according to his campaign.

Sanders wants to give at least $48 billion annually to four-year public colleges and universities, tribal colleges, community colleges, trade schools and apprenticeship programs to eliminate tuition and fees.

It’s an attractive idea to 34-year-old Alejandra Cruz, who said she’s been overwhelmed by student debt since graduating from law school in 2010. As she waited for the event to begin Friday, the El Cerrito resident said Sanders was her top choice among the crowded Democratic field.

“Now that I have a young baby, I don’t want to be worrying about paying off my loans when I’m worrying about how to pay for her college,” Cruz said as her 9-month-old daughter, Elena, tugged on her earrings.

Increasing access to higher education regardless of someone’s financial status has been a key promise in Sanders’ bid for the White House. While that promise set him apart in the 2016 primary against Hillary Clinton, many of his competitors for 2020 have also proposed some type of higher-education subsidy.

Massachusetts Sen. Elizabeth Warren, for example, also wants to fund universal free public college and cancel student loan debt, though not for those with household incomes above $250,000 a year.

“Student loan debt is a huge deal for our family, and I’d love to have a president that understands that,” Cruz said.

Sanders’ debt-canceling initiative would be funded by a tax on buying and selling stocks, bonds and derivatives.

As he sat in the crowd with his wife, Jon Edwards, 69, said he feared Sanders’ idea of “taxing the wealthy” could alienate some voters.

“Every time these progressive policies get made, there is always a loose explanation for how it’ll get funded, which leaves ammunition for the critics,” he said. Still, Edwards said he supported the idea of free tuition for public education.

Sanders said cities like San Francisco make the idea of free higher education “less radical every day.”

San Francisco was among the first cities in the country to create a free community college program, in 2017. It offers classes at no charge to all city residents regardless of age, income or educational background.

The program was crafted by former Supervisor Jane Kim, who now serves as Sanders’ Bay Area regional campaign director.

“We support Bernie, not because we like his values, but because he stands for ours,” Kim said before Sanders took the stage. “And there is no proposal more aligned with the American dream and our values than making sure college is affordable for all and canceling student debt.”

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani