It doesn't really make sense to claim the Saami have lived there for 10k years. Samic language(s) arrived in that area more like 1.5k years ago.[1] Sure, there were people there before that, but they were not "Saami" in any meaningful sense. But yeah, it's before the Finns, anyway.

[1] https://www.academia.edu/4811760/An_Essay_on_Saami_Ethnoling...