Alexandria Ocasio-Cortez’s surprise win against incumbent Joseph Crowley in the New York congressional primaries was one of this week’s more inspiring headlines. The 28-year-old democratic socialist had been written off by many mainstream pundits, who saw Crowley as the far more likely victor; after all, Crowley had served in Congress for 20 years, and the polling only weeks earlier had not been in Ocasio-Cortez’s favor. Yet, on Tuesday night, video of Ocasio-Cortez’s stunned, elated face swept across social media, as her grassroots victory inspired murmurs that the blue wave so many liberal voters have hoped for could swing even further left than anticipated come November. As she sat down with Stephen Colbert on Thursday’s Late Show, Ocasio-Cortez walked her host through the moment she realized she’d won—and the moment that made her realize she stood a real chance in the first place.

When asked how she managed to turn the race around from just three weeks before, when she was trailing Crowley in the polls, Ocasio-Cortez said, “I don’t think polling is always right.” As Colbert wryly noted, “We learned that in 2016.” But Ocasio-Cortez also knows why the polling was, at least in her case, inaccurate: “People try to identify who’s the most likely person to turn out,” she said, “and what we did is we changed who turns out—and that changes the whole electorate.”

Ocasio-Cortez recalled a moment, just eight minutes until the polls closed, when she realized something had shifted: “These two teenage-looking kids came up to me like, ‘We just voted for you!’” Ocasio-Cortez said. The two told her they were 19 years old. “I was like, ‘Oh, 19 years old, voting in an off-year midterm primary election?!’”

Later that night, the moment Ocasio-Cortez realized she had won—unseating a 10-term representative in her very first election—went viral. She had not checked the polls that day, but when she arrived at her watch party, she knew something big was happening. “It was an old billiards hall in the Bronx,” Ocasio-Cortez said. “I hadn’t checked any of the polls on my phone, and we get out, and I go, ‘Oh my God’ outside because I see all these reporters running to the watch party . . . I’m literally racing these reporters into the billiards hall, and I run inside, and I just run to this TV set and I look up and I see the margin, and then I see the amount of precincts reporting. And that’s how I found out that we won the election. Right there in that moment.”