Holden was born William Franklin Beedle Jr. on April 17, 1918, in O'Fallon, Illinois. He was the son of William Franklin Beedle (1891–1967), an industrial chemist, and his wife Mary Blanche Ball (1898–1990), a schoolteacher. He had two younger brothers, Robert Westfield Beedle (1921–January 5, 1944) and Richard P. Beedle (1924–1964).
One of his father's grandmothers, Rebecca Westfield, was born in England in 1817, while some of his mother's ancestors settled in Virginia's Lancaster County after emigrating from England in the 17th century. His younger brother, Robert W. "Bobbie" Beedle, became a U.S. Navy fighter pilot and was killed in action in World War II, over New Ireland, a Japanese-occupied island in the South Pacific, on January 5, 1944.
His family moved to South Pasadena when he was three.