A two-star prospect, Neuzil chose Appalachian State out of 12 scholarship offers.[2] His position was changed to center upon joining the school's football team.[3] As a true freshman in 2016, Neuzil redshirted.[1] In 2017, he appeared in seven games, beginning the year as backup center before being moved to starter at left guard. As a sophomore in 2018, Neuzil started all 13 games as a left guard and was selected second-team all-conference by Pro Football Focus (PFF).[1]
Neuzil was named a first-team all-conference selection as a junior in 2019, having started all 14 games as the team's left guard. In 2020, he started 12 games and was named first-team all-conference by PFF and third-team by the league's media and coaches. He was also named second-team All-American by Sporting News and PFF, and was a fourth-team selection by Phil Steele.[1] He declared for the NFL Draft following the season.[4]
After going unselected in the 2021 NFL draft, Neuzil was signed by the Atlanta Falcons as an undrafted free agent.[6] He was waived at the final roster cuts but was re-signed to the practice squad afterwards.[7][8] He was released on October 29,[9] but was then brought back on November 1.[10] After spending the entire 2021 season on the practice squad, Neuzil signed a future contract with Atlanta in January 2022.[11] He was waived at the final roster cuts again in 2022, and was then brought back as a member of the practice squad.[12] Neuzil was elevated to the active roster for the Falcons' week nine game against the Los Angeles Chargers, and made his NFL debut in the 17–20 loss, appearing on four special teams snaps.[13][14] He was promoted to the active roster on November 22, 2022.[15]
On March 3, 2024, Neuzil signed a one–year contract extension with the Falcons.[16]