Brecht attended Ankeny High School in Iowa. He was lights out in his junior and senior seasons, leading Ankeny to a state title in his senior year. In that season, Brecht held a 10-0 record with a 0.57 ERA and 126 strikeouts. He also limited hitters to a .099 batting average and had a .77 WHIP. He joined Iowa as a multisport athlete, playing football and baseball.
As a freshman, Brecht mostly came out of the bullpen to pitch. He had 17 appearances with just 1 start. He had a 3.18 ERA with 44 strikeouts and 25 walks in 22.2 innings. He got comfortable towards the end of the season, allowing just one earned run in his last 10 relief outings, spanning 13 1/3 innings with 28 strikeouts.
Brecht became a starter in his sophomore year, pitching in 17 games and making 16 starts. He had a 3.74 ERA with 109 strikeouts and 61 walks in 77.0 innings pitched. The Hawkeyes were 12-4 in Brecht's starts. Brecht earned First Team All-Big 10 honors with this performance.