I've heard quite a few mentions of the Proto Indo-European language as being the oldest language that we have evidence for with some going even further and arguing that it was the very first language spoken by human beings - with the video game Far Cry Primal being one of the many pieces of media that has helped to attest to such a hypothesis.
But how much do we really know about the language?
What evidence is there?
When and where was it spoken?
How many words, phrases or dialects are known and was it truly the very first human language?
Proto-Indo-European (PIE) is a reconstruction, we do not have any direct evidence for it, although modern linguists have written plenty of texts in that reconstructed protolanguage. Anything you see that purports to be spoken or written in PIE is an example of this modern reconstruction, it's not a reading of an actual archaeological artifact that someone found somewhere.
PIE is an important artifact of comparative historical linguistics, which analyzes languages we do have evidence of to create that reconstruction. Language change is (mostly) regular and consistent, so with enough of that evidence, you can figure out what a family's parent languages sounded like and how the various sub-families and daughter languages came to be the way they now are. PIE is, in essence, the tip of a pyramid (or the base of an inverted pyramid, as you prefer to imagine). The "lower" levels of the pyramid are the languages of the Indo-European family, inclusive of modern languages, older attested IE languages (everything from Middle French to Sanskrit), and later branch protolanguages (other unattested reconstructions such as Proto-Germanic, Proto-Italic, and Proto-Iranian). All of those various languages constitute the evidence that contributed to the reconstruction of PIE. Linguists have reconstructed protolanguages for many other families as well, but PIE remains by far the most studied.
The prevailing theory — known as the "Kurgan hypothesis" after a Russian word for a type burial mound, and substantiated at least partially by archaeological and genetic evidence as well as linguistic — is that speakers of PIE lived in and around the Pontic-Caspian steppe around 6000-7000 years ago, and the various branches of the family developed out of several waves of migrations in all directions over the course of the subsequent 2000 years or so.
The three languages/dialects heard in Far Cry Primal are interesting in that they're actually conlangs inspired by PIE. Ubisoft hired two English linguistics professors, Andrew and Brenna Byrd, as consultants. They used their own research to imagine what even earlier speakers might have sounded like.
was it truly the very first human language?
Not by a long shot. Language is generally thought to have developed 60-100 kya, an order of magnitude longer ago than PIE was spoken. I believe it's the earliest/oldest language we've systematically reconstructed, though.