Finnie's NHL career began with a flourish. He had six points (three goals, three assists) in his first seven games, becoming the first Detroit Red Wings player with as many through their first seven since Lucas Raymond (eight) and Moritz Seider (six points) in 2021-22. He scored his first two NHL goals and had an assist in a 4-2 win against the Edmonton Oilers at Little Caesars Arena on Oct. 19, 2025, becoming the first player selected by Detroit in the seventh round or later to get a multigoal game for the Red Wings since Henrik Zetterberg on Jan. 18, 2015.

The seventh-round pick (No. 201) in the 2023 NHL Draft signed a three-year, entry-level contract with Detroit on March 26, 2024, after ending his junior hockey career with 84 points (37 goals, 47 assists) in 55 games as captain of Kamloops in the Western Hockey League.

Finnie debuted with Kamloops in 2021-22, and had six assists and was plus-three with two penalty minutes in 48 games. He was among team leaders in 2023-24 with 19 goals (tied for second), 40 assists (first) and 59 points (first). He was named the WHL Player of the Week for the period ending Feb. 11 after getting nine points (seven goals, two assists) in three games. His 35 points (nine goals, 26 assists) in 64 regular-season games and seven points (four goals, three assists) in 14 WHL playoff games helped the Blazers advance to the 2023 Memorial Cup.

Before playing junior hockey, Finnie skated at Yale Hockey Academy in the Canadian Sport School Hockey League from 2018-21. The Lethbridge, Alberta, native played five games with the under-18 team during the 2020-21 season and had 107 points (51 goals, 56 assists) in 60 games at the under-15 level from 2018-20.