Cosgrove attended Monsignor Farrell High School in Staten Island, New York.
[3][4] Cosgrove spent his first professional season with the rookie–level Arizona League Padres and the Low–A Tri-City Dust Devils.
[5] He spent 2018 with the Single–A Fort Wayne TinCaps, appearing in 24 contests (21 starts) and going 3–6 with a 3.71 ERA and 122 strikeouts in 116+1⁄3 innings of work.
[6] In 2019, Cosgrove made only 9 appearances (all starts), splitting his time between the AZL Padres and the High–A Lake Elsinore Storm.
[7] He returned to action in 2021, and made 22 appearances for the Double–A San Antonio Missions, posting a 2.36 ERA with 32 strikeouts in 26+2⁄3 innings pitched.