He is a son of Ståle Solbakken. While his father was a football player and later manager, mostly abroad,[2] the family settled in Hamar and Solbakken came through the youth ranks of Hamarkameratene. He made his senior debut in 2016 and was a prolific Norway youth international, making his debut for Norway U21 at the age of 18. In the 2020 1. divisjon he passed the mark of 100 league games for Hamkam.[3]
Ahead of the 2021 season he was bought by Stabæk.[4] He made his Eliteserien debut in May 2021 against Haugesund.[3] After Stabæk were relegated, Solbakken transferred to Viking in February 2022. He signed a four-year contract with the club.[5]