He was born in Vienna, Austria, and studied music there in the Theresianum and at the Max Reinhardt Seminar. Following the occupation of Austria by Nazi Germany in 1938, Zinner and his parents, who were Jewish, emigrated. They went first to the Philippines, and in 1940 to the United States. As a young man, Zinner worked in Los Angeles as a taxi driver and occasionally as a pianist at screenings of silent films.