Bigge played collegiate summer baseball in the Northwoods League, where his fastball reached 95 miles per hour (153 km/h).
In his first professional season, Bigge logged a 1.13 ERA with 22 strikeouts in 9 games for the rookie–level Arizona League Cubs and Low–A Eugene Emeralds.
Bigge worked for a financial startup after the minor league season was cancelled as a result of the COVID-19 pandemic shutdown.
[2][5] Bigge split the 2022 campaign between South Bend and the Double–A Tennessee Smokies, accumulating a 7–2 record and 5.26 ERA with 70 strikeouts and 10 saves in 41 games.
On July 28, 2024, the Cubs traded Bigge, Christopher Morel, and Ty Johnson to the Tampa Bay Rays in exchange for Isaac Paredes.