Born in Pittsburgh, Pennsylvania, in 1921, Betz was the oldest of four children—two sons and two daughters—of Carl W. and Mary Leona Betz. His father was a native of Missouri; and according to the federal census of 1930, he was then the "chief chemist" at a local laboratory and later, by 1940, for Allegheny County. Growing up in the Pittsburgh suburbs of Crafton and Mt. Lebanon, Betz began his amateur acting career very early, at the age of 10, when he formed a theatrical company with six friends who performed plays in his grandmother's basement. After graduating from Mount Lebanon High School in 1939, he won a scholarship to Duquesne University. During the summer, Betz performed in a Pittsburgh summer stock company and decided to transfer to Carnegie Mellon University, then known as Carnegie Tech, in Pittsburgh to study drama. His education was interrupted in 1942, when he was drafted into the United States Army. He served in Italy and North Africa during World War II and eventually became a technical sergeant with the Corps of Engineers.