The Rig Veda does provide important evidence of a migration, but not by narrating it. Rather, the vocabulary, grammar, and mythological content are so similar to the Avestan texts that a common linguistic origin seems inescapable. That of course doesn't demonstrate population replacement on its own, but lacking Starlink or even homing pigeons, some kind of migration was clearly involved.
The prevalence of Steppe Ancestry in all modern day Indians should be enough to conclude that some form of migration happened.
All this politically tinged talk about supposed purity of DNA is utter nonsense.
Here’s an article that goes deeper into this:
https://eruditus.substack.com/p/sons-of-the-indus-the-indian...
Recent genetic research points to the complete opposite (at least to some extent). It might have taken just a generation or two for some individuals to get from the steppe to e.g. Britain.
As I understand it, the Bronze-Age Minoan civilization spoke an unrelated language (as evidenced by Linear A) and has a material culture relatively continuous with Neolithic Crete, not imported from the Kurgan culture. They would have been the ones experiencing the steppe-nomad-descendant invasion, the steppe nomad descendants in question being the Mycenaeans around 01450 BCE, who were at that point millennia removed from both the steppes and nomadism but presumably still rode horses at least sometimes.