Toppin played two seasons of collegiate ball at the University of Dayton, but saw a massive usage spike between his freshman and sophomore seasons. That, mixed with his prolific dunking ability, let to national attention and an eventual draft declaration as one of the league's top prospects. Toppin averaged 14.4 points, 5.6 rebounds and 1.8 assists through 33 games (15 starts) as a freshman, but those marks improved to 20.0 points, 7.5 rebounds and 2.2 assists through 31 games (all starts) as a sophomore. Toppin led the conference in field goals made (245) and field goal percentage (.633) en route to winning Atlantic Ten Player of the Year honors, but he wasn't done there. That sophomore season resulted in a full trophy case, as the consensus All-American was given Wooden Award honors, in addition to the Naismith and Karl Malone Awards. His team saw massive success as well, as the Flyers swept the Atlantic Ten conference and posted a 29-2 overall record. They were projected by many to get a No. 1 overall seed in the 2020 NCAA Tournament, but the Flyers' title hopes ended when the tournament was eventually cancelled due to the COVID-19 pandemic.