In Taylor's first season in 2020, he punted 40 times for 1,765 yards, with 18 punts being down within their opponents' 20 yard line.[3] For his performance on the year, Taylor was named the Big Ten Punter of the Year, along with being named first team All-Big Ten.[4][5] In the 2021 season, Taylor would punt 80 times for 3,688 yards, along with 38 punts being downed within their opponents' 20 yard line.[6] In week one of the 2022 season, Taylor punted ten times for 479 yards with seven punts downed inside the 20, as he helped the Hawkeyes beat South Dakota State. For his performance on the game, Taylor was named the Big Ten Special Teams Player of the Week.[7] In the following week, Taylor would punt six times for 304 yards with two punts being downed within the 20 yard line, but Iowa would lose versus rival Iowa State.[8] Taylor would finish the 2022 season with 82 punts for 3,725 yards, along with 38 punts inside the 20 yard line.[9] For his performance on the season, Taylor was named first team All-Big Ten by the media, and third team All-Big Ten by the coaches.[10] Taylor was also named first team All-American.[11][12]
Instead of declaring for the 2023 NFL draft, Taylor would decide to return for the 2023 season.[13] In week six of the 2023 season, Taylor would punt six times for 284 yards, with two of his punts landing within their opponents' 20 yard line, as he helped the Hawkeyes win their homecoming game beating Purdue 20-14. For his performance, Taylor would be named the Big Ten Special Teams Player of the Week.[14] In the following week, Taylor would punt nine times for 446 yards, while six of his punts would be downed within the 20 yard line, as he helped Iowa beat Wisconsin.[15] For his performance, Taylor would be named the Big Ten Special Teams Player of the Week, in back to back weeks.[16][17] On 1 January 2024, Taylor broke the NCAA record for most punting yards in a season, with 4,479 yards. The feat bested the previous of record of 4,138, set 85 years prior by John Fingel.[18]
Taylor was selected by the Chicago Bears in the fourth round (122nd overall) of the 2024 NFL draft, making him the highest punter selected since 2019.[22] He was also selected by the BC Lions 15th overall in the 2024 CFL global draft.[23] Taylor signed his four-year rookie contract with the Bears on 11 May 2024.[24]