Gelfman was born in Brooklyn, New York and was raised in Caldwell New Jersey where he attended grade and high school, before graduating Princeton University in 1953 with a degree in architecture. Soon after, he returned to New York where he worked for the Candida Donadio talent agency and the Feuer and Martin company. It was the latter that got him his next job as an Off-Broadway producer for the improvisational theater The Premise.
From there, he became the Vice President of New York Production for United Artists, before leaving to buy film rights for the first video cassette company Cartrivision. At that time, he also began working with