Epstein was born in Toronto, Ontario. His mother, Kathy Kacer, is a Norma Fleck Award-winning writer of children's stories about the Holocaust, and his father, Ian Epstein (born 1955), is a lawyer. He has an older sister, Gabi, an actress and jazz singer. Epstein is Jewish and was raised in Conservative Judaism. He attended Claude Watson School for the Arts in Toronto and then continued in the Claude Watson program in Earl Haig Secondary School. He attended Camp Gesher in Cloyne, Ontario for a few years.
Epstein was the lead actor in several of his school's plays and musicals, the most notable one being the Emcee in Cabaret. He started acting on screen in 1999, appearing in several made-for-television films and television series, including The Zack Files, Quints, Mom's Got A Date With A Vampire and an episode of Real Kids, Real Adventures.
He became well known after being cast in a lead role as Craig Manning on Degrassi: The Next Generation, joining the cast in 2002, in the second season of the show and continued to star in the show as a regular through seasons 2–5. Epstein indicated that the character "felt like a darker extension" of himself. He left Degrassi during the fifth season to attend the National Theatre School of Canada in Montreal and made theater his new focus. Epstein said, "One of the things I love about theatre is how raw it is. There's no faking it… I really wanted to have a base in theatre, and that kind of opened up all these doors for me." He returned to Degrassi for minor guest appearances in season 6-8.
Epstein made his professional theatrical debut in a Soulpepper Theatre Company production of Our Town. Jake has also appeared in Radio Free Roscoe.
He has been a member of several bands, such as Mind the Gap, and Funkasaurus Rex, playing many musical instruments, including the guitar and drums. Epstein also starred in The Dream, alongside a bunch of friends for the Toronto Fringe Festival in 2007. Epstein also had a small role in the 2008 movie Charlie Bartlett, with a guest appearance from former Degrassi cast member, Drake.
Epstein starred in a Ross Petty production of Cinderella, at Elgin Theatre (Toronto), from November 28, 2008 until January 4, 2009, the production also starred fellow Degrassi: The Next Generation actress Paula Brancati.
Epstein replaced Kyle Riabko as Melchior Gabor in the First National Tour of Spring Awakening, officially beginning his run on July 7, 2009.
In late 2009, he and fellow Degrassi star Jake Goldsbie guest-starred in an episode of the Canadian series Being Erica.
Also in 2009, Jake starred as Charlie Brown, or "CB", in Dog Sees God: Confessions of a Teenage Blockhead—alongside fellow Degrassi grads, Paula Brancati as "Van's Sister" (Lucy Van Pelt), Adamo Ruggiero as "Van" (Linus Van Pelt) and Mike Lobel as "Matt" (Pig-Pen).
From November 25, 2010 through January 2, 2011, Epstein starred in Ross Petty's Beauty & The Beast: The Savagely Silly Family Musical at the Elgin Theatre (Toronto).
From January 20, 2011 to January 29, 2011, Epstein costarred with his sister, Gabi Epstein in Michael Kooman and Christopher Dimond's "Dani Girl" at the Talk is Free Theatre in Barrie, Ontario.
In July 2011, Epstein played Billy's older brother in the Toronto run of Billy Elliot The Musical at the Canon Theatre.
He played Will in Green Day's Tony-winning rock musical American Idiot during the 2011-2012 North American tour. Epstein said, "I always think of American Idiot as my generation's The Who's Tommy or Pink Floyd's The Wall. American Idiot was very much like that time in the world, right after Sept. 11th...It was like a time of not knowing what to feel and that's what spawned this show."
Epstein made his Broadway debut in Spider-Man: Turn Off the Dark as the alternate for lead role Peter Parker/Spider-Man. He joined the company on December 4, 2012, and performed Saturday and Sunday matinees, with his first show having taken place on December 8 at the Foxwoods Theatre. Epstein referred to the role as a "childhood fantasy come true." He played his final performance on August 12, 2013 to begin rehearsing for a new musical titled Beautiful: The Carole King Musical, which opened on Broadway on January 12, 2014. This marked his second Broadway show in less than a year. The musical was based on Carole King's life, and Epstein portrayed her former husband Gerry Goffin. He indicated that it was not easy playing the man who broke King's heart. Epstein said, "I'm trying to make his struggle clear, so people understand why he did the things he did. He's not just a villain. I hope people see it's more complicated than that." He remained with the cast until September 21, 2014.
Many of the characters Epstein portrayed were troubled types. He said, "I'm a pretty upbeat person. I think I sometimes get cast as these brooding types because I bring light and joy, which hopefully makes them more likable.""My Window" — Music from Degrassi: The Next Generation
"Rescue You" — Degrassi Goes Hollywood: Music from the Original Movie
"Swan Song" — Degrassi Goes Hollywood: Music from the Original Movie