Christened Robert Alexander Cochran, the actor was born in Eureka, California, but grew up in Laramie, Wyoming, the son of a logger. While he appeared in high school plays, he spent more time delving into athletics, particularly basketball.
After stints as a cowpuncher and railroad station hand, he studied at the University of Wyoming, where he also played basketball. Impulsively, he quit college in 1937 and decided to go straight to Hollywood to become a star.
Working as a carpenter and department store detective during his early days, he gained experience appearing in summer stock and in the early 1940s he was given the chance to work with the Shakespeare Festival in Carmel. There he played "Orsino" in "Twelfth Night", "Malcolm" in "Macbeth", "Horatio" in "Hamlet" and the ungainly title role of "Richard III".
Cochran performed in plays in the Federal Theatre Project in Detroit. During World War II he was rejected for military service due to a heart murmur but directed and performed in plays at a variety of Army camps.,
On Broadway, Cochran appeared in Hickory Stick (1944).