Vinge played youth football for Oppsal IF.[2] In 2015 he moved on to Nordstrand, where he made his 3. divisjon debut in 2019. As the 2020 season was cancelled altogether, he did not become a regular until 2021, and then went on to Kjelsås in the 2. divisjon.[3]
Vinge made a breakthrough at Kjelsås during the 2023 Norwegian Football Cup, where he scored against Stabæk to eliminate the first-tier team.[4] He scored again in the round of 16 where Kjelsås knocked out second-tier team KFUM.[5] In the quarter-final Vinge scored the first goal in a 2–1 victory over Raufoss, securing an unprecedented cup semi-final. Vinge would not play that semi-final,[6] as he joined Stabæk on the starting day of the transfer window, 1 August 2023.[7]
Vinge made his Eliteserien debut in August against Viking, and scored his first goal in October against Sarpsborg 08.[8][1] A few months after joining Stabæk, Vinge was included in CIES Football Observatory's list over most successful dribbles per game in the European top leagues, where Vinge had a score of 6.4. TV 2 pundit Simen Stamsø Møller stated that Vinge handled the new league "surprisingly well".[9]