Baywatch’s Traci Bingham on Former Classmates Matt Damon and Ben Affleck (Exclusive)

Traci Bingham had a feeling that Ben Affleck and Matt Damon were destined to make it big in Hollywood.

The Baywatch star, 56, attended the same high school as the two Oscar winners in the 1980s, and she remembers recognizing their potential star power even back then.

“It was just one of these schools where everyone was very much into theatrics,” Bingham tells PEOPLE of their Boston-area alma mater, Cambridge Rindge and Latin School. “So I knew that people who were taking the acting classes, I knew that [Affleck and Damon] were going to go to be something huge.”

After graduating, Damon, 53, went on to Harvard University, and Affleck, 52, attended the University of Vermont before transferring to Occidental College in Los Angeles. During the early 1990s, the two friends co-wrote the screenplay for Good Will Hunting, a critically acclaimed film that would cement their status in the movie industry.

“When Matt and Ben first came out with their movie Good Will Hunting [in 1997], it was so huge. And I just knew from there, I mean, I knew they were going to be Oscar winners,” Bingham recalls of her former classmates. “So it was just very, very exciting.”

The film — in which both Damon and Affleck star, alongside Robin Williams and Minnie Driver — earned nine nominations at the 1998 Academy Awards. Williams won for Best Supporting Actor, and Damon and Affleck took home the Best Original Screenplay trophy. Since their big break, the duo went on to appear in more than a dozen other films together and co-founded a production company, Artists Equity.

Bingham shared her recollections of the actors as teens. “Matt, he was just kind of a goofball. He was always fun, he used to break dance, he always used to make people laugh, and he was just the life of the party,” she says. “Ben and Casey, his brother, I just couldn’t believe how tall he was. And he was always just so tall and so sweet.”

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The actress, who starred in the Baywatch TV series from 1996 to 1998, reminisced to PEOPLE about her own big break, landing the role of Jordan Tate. “It was a very long-winded, grueling process, but I did it,” she recalls of the audition process. “And when I booked it, I was in a room with all the producers, directors, writers, stylists — it was just crazy. And I was so nervous.”

When Bingham later received the call telling her the good news that she had been cast, it was an emotional moment for her. “I cried and then I screamed, and then I called my family, and then the mayor wanted to have a Traci Bingham parade,” she tells PEOPLE.

“And it was just this really big thing,” Bingham continues. “I knew at that point that I had made it, and I’d done something great being the youngest of seven children. It was very exciting for my family. It was a dream come true.”

She says she is particularly proud of having been the first woman of color to sport an iconic red Baywatch bathing suit and appear in the hit series. At the time, “it was considered an all-white show, and you didn’t see people of color on that show. I mean, there was one other male, a person of color, but as far as a woman wearing that swimsuit, there wasn’t any,” Bingham says.

“The NAACP, I had heard, came down on Baywatch that there weren’t any females of color on the show, lifeguards. And so they made changes,” she continues. “It was a big movement and I’m just honored that I was able to be that person and to make that change.”

Bingham shares more Baywatch memories alongside several of her former costars — including Pamela Anderson, Nicole Eggert, Carmen Electra, Jeremy Jackson and David Hasselhoff — in the four-part docuseries After Baywatch: Moment in the Sun, which premiered on Aug. 28 and is streaming on Hulu now.