[2] Undrafted out of high school, McGreevy enrolled at UC Santa Barbara where he pitched in 29 games as a reliever during his freshman season, posting a 5–1 record with six saves and was named first team All-Big West Conference and a freshman All-American by Baseball America.

[4][5] During his junior season, McGreevy became a first round prospect for the upcoming Major League Baseball draft.

[13] After eight starts in which he went 3-1 with a 2.58 ERA over 45+1⁄3 innings, he was promoted to the Springfield Cardinals of the Double-A Texas League with whom he ended the season.

[15] He returned to Springfield to open the 2023 season and was quickly promoted to the Memphis Redbirds of the Triple-A International League.

[17] He made his MLB debut that night as the starting pitcher versus the Texas Rangers, giving up one earned run and striking out three batters in a 10-1 Cardinals win.