N.B. The email exchange below may have been edited, e.g. to remove content not essential to the main point(s) or to standardize English spelling/grammar.
It would be nice to have some approximate dates, even wild estimates, for the time of PIE. 5000 years ago? 10,000? more??
An ancestral language called Nostratic, NOT constrained to "Indo-European," might be dated to 10,000 B.C. and later -- so it preceded agriculture.
One offshoot of that, called Pre-Indo-European, might be dated to 8,000-5,000 B.C. The beginnings of agriculture in the same general area are dated to ca. 8,500 B.C. That is, Pre-Indo-European is a [reconstructed] language that seems to have emerged among early agriculturalists in the Middle East/Anatolia/Black Sea area (the locale is disputed). The growth and spread of this language and its successors has been directly tied, by some, to that of western agriculture. The recently theorized inundation of the Black Sea ca. 5,500 B.C. bears an interesting correspondence to the approximate boundary between Pre-Indo-European and its primary successor.
Proto-Indo-European was the primary successor language, and may be dated in the general 5,000-3,000 B.C. time frame. (All of these languages pre-dated writing by their speakers, so none are attested by written records.) There are arguments, of course, about how Proto-Indo-European spread. An old hypothesis has peoples of distinctly [southern?] European stock migrating east/south onto the Indian subcontinent as late as 1,500 B.C., but there are others who argue for much earlier dates -- and from approx. the Black Sea area, not what we usually think of as Europe. Both migration patterns, of course, are possible (i.e., earlier and much later).
There is an extensive and sometimes lively literature on this topic. Any library should have a variety of materials. The more populist ones should be taken with the usual greater amounts of salt.