Asquith was born in Alden on March 13, 1929, and grew up in Little Valley. He graduated in 1947 from Little Valley High School, where he lettered in football, basketball, baseball and volleyball. He was named to The Post-Journal All-Star Basketball Team for the 1946-47 season.
Asquith also played baseball for the Cattaraugus Merchants from 1947 to 1951. He hit in the high .300s and also surpassed .400 while winning 75 percent of his starts on the mound.
Asquith attended Western Illinois University for two years and played on the junior varsity baseball team. In 1951 he was drafted during the Korean War, but fortunately the Army sent him to Germany where he played baseball for the Heidelberg Hawks and pitched in the 1952 G.I. World Series.