Due to Henry Davis being named Louisville's starting catcher in 2020, Rushing began playing first base and started six games for the season before it was cancelled due to the COVID-19 pandemic.[2] He appeared in 28 games in 2021, batting .254 with four home runs and 14 RBI.[3] After the season, he played in the Cape Cod Baseball League with the Bourne Braves with whom he batted .314 with six home runs over 118 at-bats and was named a league all-star.[4][5][6] After Davis was selected first overall in the 2021 Major League Baseball draft, Rushing was named Louisville's starting catcher for the 2022 season. He finished the season having appeared in 64 games, slashing .310/.470/.686 with 23 home runs, 62 RBI, and 16 doubles.[7] He was named an All-American, and ended the season as a top prospect for the upcoming MLB draft.[8][9]
Rushing made his professional debut with the Arizona Complex League Dodgers and was promoted to the Rancho Cucamonga Quakes after two games.[12] He played in 28 games for the Quakes, hitting .424 with eight home runs and 30 RBI.[13] At the end of the regular season, he was promoted to the Great Lakes Loons so he could play in the Midwest League playoffs.[14] He drove in three runs in three games in the playoffs and had two hits in nine at-bats with two walks and two hit by pitches.[15] Rushing remained with the Loons for the 2023 season,[16] where he hit .228 in 89 games with 15 homers and 53 RBI.[13] He was also selected to represent the Dodgers at the 2023 All-Star Futures Game.[17]
Rushing was selected to participate in the inaugural "Spring Breakout" minor league showcase during spring training 2024.[18] He began the season with the Double–A Tulsa Drillers and was promoted to the Triple–A Oklahoma City Baseball Club in August 2024, where it was announced that Rushing would play primarily as a left fielder.[19] Between the two levels, he played in 114 games, with a .271 batting average, 26 home runs and 85 RBI.[13] Rushing was selected as the Dodgers Branch Rickey Minor League Player of the Year for 2024.[20]