Cosgrove spent his first professional season with the rookie–level Arizona League Padres and the Low–A Tri-City Dust Devils. In 13 games (6 starts), he logged a 1–4 record and 3.22 ERA with 41 strikeouts in 44+2⁄3 innings pitched.[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. Cosgrove did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[7]
Cosgrove 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.[8] Cosgrove split the 2022 season between San Antonio and the Triple–A El Paso Chihuahuas. In a career–high 48 appearances, he registered an 8–2 record and 3.72 ERA with 82 strikeouts in 55+2⁄3 innings of work.[9] On November 15, 2022, the Padres added Cosgrove to their 40-man roster to protect him from the Rule 5 draft.[10]
Cosgrove was optioned to Triple-A El Paso to begin the 2023 season.[11] On April 26, 2023, Cosgrove was promoted to the major leagues for the first time.[12] He made 54 appearances for San Diego during his rookie campaign, compiling a 1-2 record and 1.75 ERA with 44 strikeouts and one save across 51+1⁄3 innings pitched.[13]
Cosgrove made 18 appearances for the Padres in 2024, but struggled to an 0-1 record and 11.66 ERA with 15 strikeouts over 14+2⁄3 innings of work.[14] He was optioned to Triple-A El Paso to begin the 2025 season.[15] In 4 appearances for the Chihuahuas, Cosgrove posted a 1–0 record and 7.36 ERA with 2 strikeouts across 3+2⁄3 innings pitched. Cosgrove was designated for assignment by the Padres on April 6, 2025.[16]
Chicago Cubs
On April 10, 2025, Cosgrove was traded to the Chicago Cubs in exchange for cash considerations;[17] he was subsequently optioned to the Triple-A Iowa Cubs.[18] In two appearances for Chicago, he recorded a 2.25 ERA with three strikeouts over four innings of work. Cosgrove was designated for assignment by the Cubs on August 31.[19] He cleared waivers and was sent outright to Triple-A Iowa on September 3.[20] Cosgrove elected free agency following the season on November 6.[21][22]
Houston Astros
On January 29, 2026, Cosgrove signed a minor league contract with the Houston Astros.[23]