Glass was a standout quarterback in Corpus Christi, Texas, and played in the 1947 Oil Bowl alongside Hayden Fry. He choose to attend Rice University, where he was a three-year letter-winner in both football and baseball. He captained the 1950 football team and the 1951 baseball team. He keyed Rice's drive to the 1949 Southwest Conference crown, including a 17–15 win over Texas in a showdown in Austin, Texas. Rice also won the 1950 Cotton Bowl Classic against the University of North Carolina, which was led by Charlie Justice, also known as "Choo Choo".