Wolf's 27 saves helped the Flames to a 3-2 win against the San Jose Sharks at Scotiabank Saddledome on Feb. 23, 2025. He became the fifth-fastest United States-born rookie goalie to 20 wins in a season behind Frank Brimsek (27 games in 1938-39), Ryan Miller (28 in 2005-06), Tom Barrasso (31 in 1983-84) and Jeremy Swayman (33 in 2021-22). He was named a finalist for the Calder Trophy given to the NHL rookie of the year after going 29-16-8 with a 2.64 goals-against average, .910 save percentage and three shutouts.

The goalie broke into professional hockey full time in the 2021-22 season when the seventh-round pick (No. 214) of the Calgary Flames in the 2019 NHL Draft went 33-9-5 with a 2.35 GAA and .924 save percentage in 47 games for Calgary's former American Hockey League affiliate in Stockton and helped the team reach the Western Conference Final of the Calder Cup Playoffs. He was also named to the AHL All-Rookie Team, the First All-Star Team and chosen as the league's top goalie.

Wolf topped that performance in his second pro season. His 55 games led all AHL goalies and he finished 42-10-2, ranking first in the league in wins, GAA (2.09), save percentage (.932), and shutouts (seven). He became the eighth goalie in AHL history to win league most valuable player and first since Jason LaBarbera in 2004. He again was named to the First All-Star Team and chosen as top goalie, becoming the first-ever repeat winner of the award.

Wolf made his NHL debut with the Flames with 23 saves in a 3-1 win against the Sharks on April 12, 2023, nearly three years after he signed his entry-level contract with Calgary on May 1, 2020. He ended his Western Hockey League career 106-34-6 with a 1.84 GAA, .935 save percentage and 24 shutouts in four seasons for Everett, and 5-5 with a 1.99 GAA, .915 save percentage and one shutout in 11 WHL playoff games.

He signed a seven-year, $52.5 million contract ($7.5 million average annual value) with the Flames on Sept. 9, 2025.