I don't have a strong opinion on the matter, evidence is very sparse. There is a strong consensus that Basque is not Indo-European. It is also seems likely that the Basque language (or an ancestor) was used in the surrounding area before the large Indo-European migration from the east, Basque doesn't seem to have been brought by a different migration from somewhere else, at least not after pre-history.

The Vasconic Substrate Hypothesis suggests that Basque was a major language in Europe from prehistory or at least the neolithic, and that it influenced most modern European languages. That's rather a stretch, modern western European languages are mostly a mix between Indo-European variants and Latin, to a larger or smaller degree. Claiming another pre-indo-european layer under all that, I mean, sure, maybe, but it is diluted to an extent that makes it rather irrelevant.

The evidence for that is very weak, it depends how literally you interpret it. I think it is arrogant to suggest that those ancient languages were basque, rather modern basque has some distant roots in those pre-into-european languages. In my opinion, the more correct way of expressing it would be that this proto-basque was part of a large family of related languages spoken in Europe during the neolithic. There is no proper evidence that proto-basque was widespread, it's just that it is the only preserved remnant from that linguistic era at large.