Epstein made his professional stage debut in a production of Our Town, which played at the Royal Alexandra Theatre in 1999. After this, Epstein played the Artful Dodger in a production of Oliver!. The musical played at the Princess of Wales Theatre between November 2, 1999 and January 2, 2000.

In 2009, he starred as C.B. (Charlie Brown) in a Canadian production of Dog Sees God: Confessions of a Teenage Blockhead. Later that year, Epstein joined the first national tour Spring Awakening, where he replaced Kyle Riabko as Melchior Gabor. His first performance with the tour was on July 7, 2009, and stayed with the tour until it ended in 2010.

In July 2011, Epstein joined the original Canadian production of Billy Elliot the Musical. He played the role of Tony Elliot, Billy's older brother, in the production which played at the Canon Theatre in Toronto. After that show closed, Epstein played Will in the first national tour of American Idiot, which began in December 2011. In a 2013 interview, Epstein said that Will was the most challenging role had had ever played. He said, "I sat on a couch and never left the stage for the majority of the show. That experience was a whole lesson in pacing, in creating a whole world for yourself on stage

In 2012, Epstein made his Broadway debut in Spider-Man: Turn Off the Dark, which played at the Foxwoods Theatre. He was the alternate for the lead role of Peter Parker/Spider-Man. Epstein referred to the role as a "childhood fantasy come true.