As a true freshman in 2021, Retzlaff threw for 3,302 yards and 23 touchdowns before deciding to transfer to Riverside City College.[3][4] The following season with Riverside, he started 13 games, recording 4,596 yards passing, and 44 touchdowns, in addition to setting the school record for most passing yards in a game (529) and passing touchdowns in a single game (6).[5][6] He entered the transfer portal for the second time at the season's end.
As the number one rated junior college quarterback in the nation, Retzlaff announced in January 2023, that he would be transferring to BYU.[7][8] Entering the 2023 season, he was named the second-string quarterback behind Pittsburgh transfer Kedon Slovis.[9] After an injury to Slovis, Retzlaff was named the starting quarterback against West Virginia.[10][11] In his first career start, he threw for 210 yards in a 37–7 loss.[12] The following week, he was once again named the starting quarterback.[13][14] In his second career start against Iowa State, he threw his first career touchdown pass at the FBS level in a 45–13 defeat.[15] Retzlaff finished the season throwing for 648 yards and three touchdowns, while also rushing for 116 yards and three touchdowns.[16]
Entering the 2024 season, Retzlaff competed with Gerry Bohanon for BYU's starting quarterback job, eventually being named the week one starter.[17] In the season opener against Southern Illinois, he threw for 348 yards and three touchdowns in a 41–13 victory.[18] Against Oklahoma State, Retzlaff threw for 218 yards and two touchdowns, including the game-winning 35-yard touchdown pass to Darius Lassiter, while also rushing for 81 yards and a touchdown in a 38–35 win.[19]
Retzlaff is Jewish.[20] In 2023, he became the first ever Jewish quarterback to play at BYU.[21][22][23] In 2024, Retzlaff signed an NIL deal with the Jewish food brand Manischewitz, becoming the first athlete to do so.[24]