It is very misleading to draw a link between the Sami people and the prehistoric peoples that first ventured into Northern Scandinavia at the end of the last Ice Age. No such link exists.
The ancestors of Sami people arrived from east around 1500 BCE (not significantly earlier than the ancestors of "non-indigenous" people of the area). The Sami language was developed much later.
While the common ancestor of the Saami languages came from the east, it spread in part by the local inhabitants adopting the language of outsiders. To a degree, the Saami are the same prehistoric peoples, they simply switched to speaking Saami. This is also why the Saami language is replete with words not found in other languages of the Uralic family: when the indigenous people learned Saami, they brought many of their original language’s words into their new language.
The ancestors of Sami people arrived from east around 1500 BCE (not significantly earlier than the ancestors of "non-indigenous" people of the area). The Sami language was developed much later.