Although the Indo-Europeans settled in new lands, in some cases (such as Greece) evidently by conquest, they did not always dominate the local people in the beginning. Instead, they often served the local peoples as mercenary warriors, or came under their domination in general. In either case, the Indo-European migrants—who were mostly men—married local women and, by mixing with them, developed their distinctive creole dialect features. The most influential of the new dialects was Proto-Indo-Iranian, the speakers of which appear to have been influenced linguistically by a non-Indo-European people from whom the Indo-Iranians borrowed their distinctive religious beliefs and practices.

Beckwith, Christopher I.. Empires of the Silk Road: A History of Central Eurasia from the Bronze Age to the Present (p. 32). Princeton University Press. Kindle Edition.

The traditional theory that Indo-European developed into its attested daughter languages over many millennia in the Proto-Indo-European homeland is essentially impossible typologically. It has recently been contested, and a more likely “big-bang” type of split proposed instead, such as the one historically attested later for the spread of Turkic and Mongolie26 The old theory is essentially disproved also by the fact that, if the Indo-European daughter languages had already been fully developed before the migrations, there would be evidence of early Greek, for example, in Iran, or Russia; evidence of Germanic in India or Italy; evidence of Tokharian in Greece or Iran, and so on. But there is no such evidence. Leaving aside much later, historically attested migrations, Anatolian is known only from Anatolia, Greek only from Greece, Tokharian only from East Turkistan, Germanic only from northwestern Europe, Armenian only from Armenia, and so on. The only possible exception is Old Indic, which is attested first in upper Mesopotamia and the Levant, and later in India. Although it is assumed that the Iranian expansion into Persia is responsible for splitting the Old Indic–speaking people into the two attested branches, even in this case there is no evidence for Indic ever having been spoken in Europe, say, or northern Eurasia. Proto-Indo-European was spoken in the Central Eurasian homeland, while the attested daughter languages were spoken in their attested homelands outside it, where they developed as creoles almost instantaneously after their introduction there. The scenario presented here thus accords with typology, the recorded history of language development and spread, and with the actual attested situation of the Indo-European daughter languages.

Beckwith, Christopher I.. Empires of the Silk Road: A History of Central Eurasia from the Bronze Age to the Present (p. 35). Princeton University Press. Kindle Edition.