In Taylor's first college season in 2020, he punted 40 times for 1,765 yards, with 18 punts being down within their opponents' 20 yard line.[5] For his performance on the year, Taylor was named the Big Ten Conference's Punter of the Year, along with being named first team All-Big Ten.[6][7] In the 2021 season, Taylor punted 80 times for 3,688 yards, along with 38 punts being downed within their opponents' 20 yard line.[8]
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; he was named the Big Ten Special Teams Player of the Week.[9] 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 to rival Iowa State.[10] Taylor finished the 2022 season with 82 punts for 3,725 yards, along with 38 punts inside the 20 yard line.[11] 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.[12] Taylor was also named first team All-American.[13][14]
Instead of declaring for the 2023 NFL draft, Taylor decided to return for the season.[15] In week six of the 2023 season, Taylor punted 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.[16] In the following week, Taylor would punt ten times for 506 yards, while six of his punts would be downed within the 20 yard line, as he helped Iowa beat Wisconsin.[17] For his performance, Taylor would be named the Big Ten Special Teams Player of the Week, in back to back weeks.[18][19] In the 2024 Citrus Bowl, 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.[20]
Despite his position, Taylor was widely credited with helping Iowa remain competitive amid anemic performances by the offense. His punts regularly pinned the receiving team deep on their own side of the field, which allowed Iowa's top-ranking defense to prevent their opponent from scoring and keep games close. In 2023, the offense averaged 16.6 points per game (fourth worst in the country) but went 10–3 with the majority of the wins coming in what USA Today writer Craig Meyer described as "low-scoring games in which the fight for field position was paramount."[21] His total punting yardage that year also exceeded the 3,296 recorded by Iowa's offense as well as 33 other schools.[4][22]
For his contributions in 2023, he received the Ray Guy Award for the best punter in the country, was named a unanimous first-team All-American, and became the only multi-time winner of the Big Ten Punter of the Year.[23][24][4] A coach also gave Taylor a first-place vote for that season's Chicago Tribune Silver Football, given to the best player in the Big Ten as voted upon by coaches.[25]
Taylor ended his career with the FBS record for most average yards per punt at 46.3. He also led the subdivision in punts within the 20-yard line in his final three years.[26]
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 and the highest by the team since Todd Sauerbrun was picked in the second round in 1995.[30][26] He was also selected by the BC Lions 15th overall in the 2024 CFL global draft.[31] He signed his four-year rookie contract with the Bears on 11 May 2024.[32]
In Week 4 of the 2024 season against the Los Angeles Rams, Taylor pinned three of his five punts inside the 10-yard line.[33] His role pinned the Rams and helped the Bears' "takeaway-crazed" defense seal the 24–18 win: Taylor's final punt with 1:13 remaining placed the Los Angeles offense at their own 8, meaning they would have needed to drive 92 yards to score the tying touchdown, but it ended with an interception.[34][35] Taylor earned NFC Special Teams Player of the Week.[33]