Linguistically, even though the sami language has ties to finno-ugric, this is most likely due to an areal influence on Sami from Finnic stemming from the wave of the Finno-Karelian agricultural expansion. I'm not aware of any linguistically consensus placing the urheimat of finno-ugric in Siberia, so not sure where you get that from.

Genetics show us another picture, which is that samis are a mix of several different peoples, and primarily a blend of two populations known as European Hunter Gatherers (who settled the continent in the Upper Paleolithic) and the Ancient North Eurasians. The "Mongoloid" and Siberian origins has been largely discredited for several years now. Genetic research showed that Sami are an isolated branch of every other group around them (including finno-ugrics).

Lastly I don't think anybody is proposing that the samis are indigenous to the whole of Scandinavia, but rather northern Scandinavia – as there isn't much evidence of Sami settlement in the south of Norway and Sweden or Denmark for that matter. Archealogical finds show that the Sami were in northern Fennoscandia before any other present group.