Cohen was born in Manhattan,[2] the only child of Donna (née Ackerman), a director of a preschool, and Noel Cohen, a music teacher.[3] He is Jewish,[4][5] a fourth generation New Yorker whose ancestors emigrated from Russia.[6][7] Cohen made his stage debut as Mr. Peachum in a school production of The Threepenny Opera.[8] He graduated from Elisabeth Irwin High School in 2008 and received a full scholarship to study acting at University of Arts in Philadelphia.[9] He trained at UArts for two years before dropping out to study acting in New York.[10]