Yes indeed. The Hobbits do not even begin to migrate from their ancestral homeland east of the Misty Mountains toward Eriador (northwestern Middle-earth where the Shire is located) until ~1000 years into the Third Age, and the Shire isn't established with the permission of the Kings of Arthedain (Aragorn's ancestors) until about 500 years after that.

The Amazon series is ostensibly set in the Second Age, literally millennia before any Hobbit should appear in the lands of the Dúnedain. Much less a black Hobbit, when (being a sub-race of Men) they consistently lived in the far north of Middle-earth and before migrating, were longtime neighbors of the famously blond & pale-skinned Northmen who would later become the Rohirrim.