In 2021, Braxton appeared in four games and took a redshirt.[2] In week 11 of the 2022 season, he made his first collegiate start, where he completed 13 of 25 passes for 146 yards and a touchdown and rushed for 32 yards in a loss to Tulane.[3] During the 2022 season, Braxton completed 92 of 163 pass attempts for 1,133 yards and ten touchdowns and rushed for 145 yards and five touchdowns, earning Freshman All-America honorable mention by College Football Network.[2] After the season, he entered his name into the NCAA transfer portal, but later withdrew his name and returned to Tulsa.[4] In 2023, Braxton suffered through injuries, where he completed 22 of 50 passes for 222 yards and two touchdowns with six interceptions, while also rushing for 174 yards.[5] After the season, he entered his name into the NCAA transfer portal.[2]
Marshall
Braxton transferred to play for the Marshall Thundering Herd.[6] In 2024, he started eight games, where he threw for 1,624 yards and 19 touchdowns with two interceptions, completing 60.2% of his passes, while also adding 610 yards and four touchdowns on the ground.[7] Braxton was named the Sun Belt newcomer of the year and second-team all-Sun Belt.[8] After the season, he entered his name into the NCAA transfer portal.[9]