'Back to the Future: The Musical's Casey Likes Says Mom 'Always Compared Me to' Michael J. Fox (Exclusive)

For Back to the Future: The Musical star Casey Likes, comparisons to Michael J. Fox began long before he was cast as Marty McFly on Broadway.

The actor, 21, tells PEOPLE he does not "really remember a time in my life without Back to the Future," considering the 1985 movie classic released over a decade before he was born.

"I’ve watched it a million times and my mom just loved Michael J. Fox and always compared me to him," he says. For Likes, the film remains "required viewing as generations grow older" as he explains he feels most people his age were introduced to Back to the Future via their parents.

"For my generation, with parents who grew up with this movie and movies like it in the 1980s, like [E.T. the Extra Terrestrial] and all these magical, magical films in the '80s, this was required viewing," he says. "My entire generation knows about it because of our parents. I love it deeply."

Fox, now 62, saw his star rise to Hollywood's brightest heights when Back to the Future hit theaters in 1985, years after he first moved to Los Angeles as a teenager in search of an acting career.

The actor's portrayal of Marty, a high school student and musician who accidentally travels back to the year 1955, brought about decades of success for Fox.

"Most of us fresh out of acting school were just basically kind of green with envy that we weren't Michael J. Fox," Likes's costar Roger Bart, who plays Doc Brown in the musical, tells PEOPLE of seeing Fox in Back to the Future in 1985. "Because he was our contemporary, but far better looking than all of us and much more talented."

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Likes cites Back to the Future’s arrival on Broadway as similar to what he remembers his mom, former Broadway performer Stephanie Likes, telling him about what it felt like when productions like The Lion King or Rent first arrived in New York City.

"These are magical shows with such big spectacle that we're kind of doing things onstage that had never been done before. It feels really nice to be a part of a show that brings magic to families," he says. "It's a really magical show and it's kind of inspiring because [I] go to the stage door every night and there's little kids that want to be involved in theater or this was their first show."

"It's one of those moments that I think is kind of reinvigorating Broadway a little bit, and I feel really fortunate to be a part of that," Likes adds.

Back to the Future: The Musical is playing at New York City's Winter Garden Theatre now.