Cohen was born in Mountain View, California and raised in Palo Alto, California, where his family settled after living for a number of years in Israel. He is of Yemenite, Russian, and Israeli descent. Cohen graduated from the University of California, Berkeley with a BA degree in Integrative Biology. Foregoing earlier plans of attending medical school, he instead pursued professional acting.
Cohen worked for a few years at regional theaters such as The Magic, Marin Shakespeare Company, Marin Theatre Company TheatreWorks, San Francisco Shakespeare Festival, and PCPA Theaterfest. He then next moved east and earned an MFA degree in acting from the Professional Actors Training Program at Rutgers University's Mason Gross School of the Arts, where he studied under New York Acting teachers William Esper, Maggie Flanigan and Deborah Hedwall. He later moved to Los Angeles, where he performed at theaters including South Coast Repertory and began his career in film and television.