You're aware that both European languages and Sanskrit have a common ancestor, Proto-Indo-European? That's how you find identical wordstems like "Pa" for father in both (if I remember the example correctly). Something as basic as soup would be easy to imagine going back to PIE no?
So if you don’t accept PIE, what‘s the model you accept? Did Indian and European peoples migrate out of Africa separately according to your model? Using languages to analyze this is indeed a crude tool, but we have something better now: DNA evidence. And so far I at least never heard of DNA being used to disproof the Indo-European relationship, as opposed to some other hypothetical proto-people like Finno-Ugric-Mongolian-Korean-Japanese, whathever the name for that was.
You seem to be a bit emotionally attached to this? I for one like imagining that such a vast and diverse bunch of peoples may go back to just a couple of families crossing deserts, jungles and plains together.
how europeans got their language is not our problem
neither the yamnaya r1b z2103 nor sintashta r1a z2125 amounted to much in world history and the sintashtans were just scythians or what we called shakas
these geneticists are just looking for keys under the streetlight ignoring actual evidence
rest of the dna debate is massively hyped propaganda and search for relevance and funding