Peck was born in New York City, New York, where he attended P.S. 40 and The Professional Performing Arts School. His parents were unmarried at the time of his birth and he has never met his biological father. He grew up with his mother, Barbara, who is a career coach, and his maternal grandmother. Peck is Jewish, and had a Bar Mitzvah ceremony. He had asthma during his childhood, and often stayed indoors watching old sitcoms. He was inspired to become involved in stand-up comedy when he was eight years old.