Massa excelled in several sports for Holy Cross, especially on the baseball diamond, where he played catcher and first base. During his senior year in 1957, he drove in 19 runs in only 19 games, to rank second on the team. Massa also had an excellent season in 1955, leading the team with three homers and 15 runs batted in, as Holy Cross went 13-4 and advanced to the NCAA Tournament. Overall, the Crusaders posted in impressive 42-11 record during Massa's three years on the team.
On the gridiron, Massa started at both center and linebacker, with Holy Cross going 14-14-1 overall during his career.
He also joined the basketball team as a walk-on during his senior year, providing added depth after the Crusaders suffered several injuries to low post players.
Following his time at Holy Cross, Massa was drafted by the Chicago Cubs in baseball and the New York Giants in football. He spent several seasons in the Cubs minor league organization, while going 7-for-17 at the plate during a brief stint in the major leagues in 1957 and 1958.