Schmid became the fifth rookie goalie in NHL history with a shutout in Game 7 when he helped the New Jersey Devils win a Stanley Cup Playoff series for the first time in more than a decade with a 4-0 victory against the New York Rangers in the 2023 Eastern Conference First Round. He also shut out the Rangers 4-0 in Game 5, making him the 10th rookie goalie with multiple shutouts in a single series and first since Matt Murray for the Pittsburgh Penguins in the 2017 Stanley Cup Final. The only one with more is Frank McCool for the Toronto Maple Leafs in the 1945 Final.

Schmid is the second goalie in Devils/Colorado Rockies/Kansas City Scouts history to win each of his first two playoff appearances (Chris Terreri in 1990) with 22 saves to defeat the Rangers 3-1 in Game 4. He made 35 saves in his NHL postseason debut, a 2-1 victory in Game 3, and at age 22 was the third rookie to start a playoff game in New Jersey history, joining Sean Burke (1988) and Hockey Hall of Famer Martin Brodeur (1994).

Schmid ended the 2022-23 regular season 4-1-2 with a 2.02 goals-against average and .925 save percentage in his final nine games (seven starts) and was 9-5-2 with a 2.13 GAA, .922 save percentage and one shutout in 18 regular-season games (14 starts). Two years before debuting in the NHL playoffs, Schmid was playing junior hockey for Sioux City in the United States Hockey League, going 22-13-1 with a 2.01 GAA, .921 save percentage and three shutouts. He was first in the USHL in GAA and save percentage and helped Sioux City reach the Clark Cup Playoffs. Schmid played 38 games with Utica in the American Hockey League in 2021-22, including making one postseason start, a 4-3 overtime loss to Rochester in the Calder Cup Playoffs.

Schmid was traded to the Vegas Golden Knights with forward Alexander Holtz on June 29, 2024, for forward Paul Cotter and a third-round pick in the 2025 NHL Entry Draft. He made 24 saves for his first shutout with the Golden Knights in a 1-0 win against the Detroit Red Wings at T-Mobile Arena on Nov. 4, 2025.

Chosen in the fifth round (No. 136) of the 2018 NHL Draft, Schmid signed a three-year, entry-level contract with the Devils on May 17, 2021. He made 25 saves in his NHL debut, a 4-2 loss at the New York Islanders on Dec. 11.

The native of Bern, Switzerland, was named to Team Switzerland's roster for the Olympic Winter Games Milano Cortina 2026 and played for his country twice at the IIHF World Junior Championship (2019, 2020). He was teammates with future Devils captain Nico Hischier on the 2017 under-18 team.