Colorado picked Annunen in the third round of the 2018 draft and is viewed as the potential future in net for them. The 20-year-old netminder was spectacular in the Finnish Elite League in 2019-20, going 15-5-3 while leading the league in both GAA (1.77) and SV% (.920). He also represented Finland at the World Juniors in 2020, where he finished the tournament with a 2.65 GAA and .916 SV% in six starts.