Monheim was a three-year starter at Moorpark High School in California and was named Los Angeles Daily News All-Area first team and All-Camino League Co-Offensive Lineman of the Year as a senior offensive tackle and guard. He made the 2019 PrepStar All-American team and committed to USC during his senior year.
He appeared in one game as a freshman, getting a bulk of the playing time at right guard against Washington State. In 2021, Monheim saw action in all 12 games on the offensive line and on special teams, starting the first seven games at right tackle.
In 2022, he started all 14 games, 11 games at right tackle and three games at right guard. He was very productive on the line for the Trojans and was named All-Pac-12 Honorable Mention.
Monheim stated all 13 games protecting Caleb Williams at left tackle during the 2023 season. After the season, Moneheim announced he will be coming back to USC.