As a freshman at Georgia in 2018, Hancock started 15 games, going 6–4 with a 5.10 ERA and 75 strikeouts in 77 2⁄3 innings.[3][4][5] As a sophomore in 2019, he went 8–3 in 14 starts with a 1.99 ERA and 97 strikeouts in 90+1⁄3 innings.[6] After the season, he was invited to play for the USA Baseball Collegiate National Team.[7] He made four starts in 2020 before the season was cancelled due to the COVID-19 pandemic.
Hancock made his professional debut in 2021 with the Everett AquaSox of the High-A West.[10] In June 2021, Hancock was selected to play in the All-Star Futures Game.[11] He was promoted to the Arkansas Travelers of the Double-A Central in August.[12] Over 12 starts between the two teams, he went 3-1 with a 2.62 ERA and 43 strikeouts over 44+2⁄3 innings.[13] He missed time during the season due to a shoulder injury.[14] In 2023, Hancock returned to Arkansas, making 20 starts and posting an 11–5 record and 4.32 ERA with 107 strikeouts across 98.0 innings pitched.[15]
On August 9, 2023, the Mariners selected Hancock's contract and promoted him to the major leagues.[16] He made his MLB debut that day as the starting pitcher versus the San Diego Padres. He pitched 5 innings, giving up 2 hits, 1 earned run, 3 walks and 3 strikeouts. On August 20, Hancock was removed from a start against the Houston Astros with a right shoulder strain.[17] He was subsequently placed on the injured list the next day.[18] On August 22, Hancock was transferred to the 60–day injured list, ending his season. In 3 starts for Seattle during his rookie campaign, he logged a 4.50 ERA with 6 strikeouts in 12.0 innings of work.[19]