As your Wiki link states -

"Though geographically surrounded by Indo-European Romance languages, Basque is classified as a language isolate. It is the last remaining descendant of the pre-Indo-European languages of Western Europe. Consequently, its prehistory may not be reconstructible by means of the comparative method except by applying it to differences between dialects within the language. Little is known of its origins but it is likely that an early form of the Basque language was present in Western Europe before the arrival of the Indo-European languages to the area.

"Some authors have noted that the words for "knife" (aizto), "ax" (aizkora) and "hoe" (aitzur) seem to derive from the word for "stone" (haitz), and have therefore concluded that the language dates to the Stone Age or Neolithic period, when those tools were made of stone; others find this unlikely; see the aizkora controversy."

The salient points here being A) that Basque is the last remaining descendant of the pre-Indo-European languages of Western Europe – not that it is (western) Europe’s first language, nor B) that it’s descended from non-European languages. Native languages spoken in places like Australia may, therefore, be far older than Basque or even Indo-European or proto-Indo-European.