From December 2011 Solheim took part in FIS races and national championships. In February 2013 he was a participant of the European Youth Olympic Festival in Brașov , where he finished 9th in slalom. Gradually, a specialization in the technical disciplines emerged. His first appearances in the European Cup and the Nor-Am Cup took place in December 2015, but were still not very successful. He began to make significant progress in winter 2016/17. He became Norwegian Slalom Junior Champion in December 2016 and won an FIS race for the first time two months later. Towards the end of the 2017/18 season, he was also able to establish himself in the European Cup. Solheim won a European Cup race for the first time on December 5, 2018, a giant slalom in Funäsdalen.
Solheim made his debut in the World Cup on December 8, 2018 in the giant slalom in Val-d'Isère , where he was eliminated in the first run. He scored World Cup points for the first time on January 12, 2019 with 22nd place in the giant slalom in Adelboden . Almost a year later, on January 11, 2020, he achieved his best result to date with 9th place in the giant slalom.