Before the 2022 NHL Entry Draft, Cooley ranked between second and fifth by sports media among draft prospects.[3][4][5][6] He was drafted third overall by the Arizona Coyotes.[7] In May 2023, he announced that he intended to return to Minnesota for the following season.[8] Despite his previous announcement of returning to Minnesota, Cooley signed a three-year, entry-level contract with the Coyotes on July 27, 2023.[9] Cooley impressed during the Coyotes 2023 training camp[2] and made the opening day roster, playing in his first NHL game, a 4–3 shootout win over the New Jersey Devils. Cooley had two assists in the game, setting up the game-tying goal by Nick Schmaltz.[10] Cooley scored his first NHL goal against Lukáš Dostál of the Anaheim Ducks in a 4–3 loss on November 1.[11]
Shortly after the end of the 2023–24 regular season, the Coyotes' franchise was suspended and team assets were subsequently transferred to the expansion Utah Hockey Club; as a result, Cooley became a member of the Utah team.[12]
Cooley is from the borough of West Mifflin in the greater Pittsburgh area. With his third-overall selection in the 2022 NHL Entry Draft, he became the highest-drafted player to date from the Pittsburgh area, surpassing previous first-round picks J. T. Miller (15th overall) and R. J. Umberger (16th overall).[14]