Peters attended Avon High School in Indiana, where he played football and basketball. He led Avon to a regional football title as a senior in 2015, participating in 13 games and completing 218 of 363 passes for 3,103 yards, 37 touchdowns, and five interceptions. He also rushed for 754 yards and 11 scores. Peters originally signed with Wisconsin out of high school, but he never ended up attending that university. He eventually landed at Purdue, where he started all 14 games as a true freshman in 2016 before being sidelined by an injury for the final three games of the season. He returned for 2017 and made eight appearances, completing 60 of 104 passes for 804 yards, seven touchdowns, and four interceptions. During his college career, Peters worked his way up the depth chart at Purdue and was given the opportunity to start as a junior in 2018. He responded by leading the Boilermakers to an 8-0 record and their first No. 1 ranking in the AP Poll, finishing the year with 3,719 passing yards, 28 touchdowns, and nine interceptions. After his successful college career, Peters entered the 2019 NFL Draft. He went straight from college to the NFL, playing in all 16 games for the Atlanta Falcons as a rookie. He completed 62 of 102 passes for 772 yards, six touchdowns, and two interceptions.