[8][9] He was named midseason All-American by the Associated Press and Sporting News after leading the Badgers in sacks (6), tackles for loss (10.5), and forced fumbles (2) through the first six games of the season.

[15] Baun made his debut on September 21, 2020, on Monday Night Football against the Las Vegas Raiders, playing on special teams.

In Week 1 of the 2024 season, he recorded 15 total tackles and 2 sacks in his first career multi-sack game in a 34–29 win over the Green Bay Packers in São Paulo, Brazil.

[21] In addition, Baun was named a member of the Associated Press First Team All Pro and nominated for Defensive Player of the Year.

[23] He earned his second postseason interception against the Kansas City Chiefs in Super Bowl LIX, leading to an Eagles touchdown two plays later.