"the same way Indo-European wiped out almost every older language in Europe (except Basque, Finnish/Hungarian)"

First of all Uralic languages arrived in Europe after Indo-European language arrived. So around 10 000 years ago, where they mostly were staying in eastern corner of Europe for most of the time. Finnish ethnicity developed under Swedish occupation(before that what is now known as Finland was populated by Karelians), so it is ~ 9th-10th century. Hungarians arrived in central Europe around the same time - around 10th century. ^ They both are very late and one of latest linguistical developments in Europe. There are certainly even younger language developments, but these are one of the youngest "historical" Europeans.

Basque is not older language of Europe, that predates IE. It is most probably one of the remnant IE languages or IE transitional languages from earliest IE waves, as current IE languages in Europe are from 3000 years old IE update.

Indo-Europeans(IE) themselves did not came to Europe - they actually formed in Eastern Europe(and then spread across to Asia - including Southern Asia - where Indo part is). We do not know what language ancestors of IE were speaking in shores of lake Baikal 30 000 years ago and before, but in Europe they were present from the time period when ice sheets were expanding in the world and which most probably drove them to Europe.

Ancestors of IE were already there from the earliest history of Europe - mainly in eastern part of Europe, where they were present from long before, but also in rest of Europe they were from Ice Age - long before arrival of genocidal Anatolian Farmers, that they eventually assimilated as well.