Wolford was born in Dallas, Texas, and moved to Jacksonville at an early age where he attended Bishop Kenny High School.

[2][3] As a pro-style quarterback, he was rated a three-star recruit by Rivals.com[4] and ESPN[5] and committed to play college football at Wake Forest.

He was briefly the all-time leader in all major statistical passing categories for high school football in the state of Florida.

[citation needed] Wolford started his college career as the first Wake Forest player to start all 12 games as a true freshman, setting school records in attempts, passing yards, touchdowns, and completion percentage by a true freshman.

[10] He was released from the practice squad a day later to make room for former New York Giants quarterback Davis Webb.

[16] He was waived during final roster cuts on August 31, 2019,[17] but was signed the next day to the Rams' practice squad.

[19] Wolford would become the first quarterback to make his first start with a team during Week 17 with a playoff berth on the line since Kyle Orton with the Dallas Cowboys in 2013.

[20] After throwing an interception to Cardinals linebacker Jordan Hicks on his first pass attempt of the game, Wolford quickly turned things around, completing 22 of 38 passes for 231 yards while also rushing six times for 56 yards as the Rams went on to beat the Cardinals 18–7 to clinch a playoff berth.

Wolford also remained the backup during the Rams' playoff run, winning Super Bowl LVI when they defeated the Cincinnati Bengals.