Cox, 31, said she is honored to star in Netflix's Orange Is the New Black, which was nominated for best television series, comedy or musical, at the Golden Globes on Sunday.
"Well first of all Orange is the New Black in so many ways I feel is the little show that could," she told PEOPLE. "There's never been a cast as diverse as ours when it comes to representing women on television, and I'm just really happy to be part of a show that has such diversity and tells such compelling human stories, but also it's touched so many people all over the world."
The actress said that she's simply trying to enjoy every minute of working on the show – no matter how small or big a moment it may be.
"To be a part of something that not only means so much to people but also gets critical acclaim and gets nominated for a Golden Globe is like a dream come true," she said. "I'm very aware this year that it might not last forever, so I'm trying to enjoy it."
She hit the red carpet in a stunning white gown and wore her hair pulled back to show off her sparkling earrings for the award ceremony.
Cox also spilled some major secrets about the upcoming fourth season of the show, revealing that her character's storyline is more relatable than ever.
"Sophia being placed in solitary confinement is such a real reality that a lot of trans people experience every day in prison, so I love that we go there and deal with this issue," she said.
The 73rd annual Golden Globes, hosted by Ricky Gervais, were presented live from Beverly Hilton Hotel in Beverly Hills, California, on NBC.