We're talking about a much longer period of time than 1000 years. Like, 4.5 billion years. Or at least 500 million.
People who speak Indo-European languages such as English, Hindi, and Portuguese descend from migrants from the Caspian steppe. Do they have strong Caspian steppe affinities? And that's only been about 4000 years.
We're much better at recording history nowadays though.
People seem to find the Yamnaya culture interesting, we just know rather little about it.
Nowadays we have ubiquitous, effortless recording and copying capabilities. The struggle for historians will be to sort through all the data in order to identify a coherent narrative.