The oldest known Indo-European texts are (in time order) the Sanskrit, Hittite, and possibly Linear A (and other) languages. Linguists have reconstructed Proto-Indo-European. However, let's say that a group of archaeologists went to, say the area around the Caspian Sea, and found cuneiform inscriptions hidden under four feet of material which are written into wood that is unusually well preserved. Then, the inscriptions are dated and found to be (say) 6750 years old with carbon-14 dating. The archaeologists are generous, and the hieroglyphs are uploaded to the Internet. They are then decoded as PIE or something similar and they are found to encode information about the dead (The message says something along the lines of "keep this soul safe"). This has not happened and is not likely to happen, but, what would the ramifications of this genuinely happening be?
The ramifications would be huge. Established hypotheses would be confirmed, rejected or have to be modified. Examples are the discovery that Hittite and the other Anatolian languages were IE (which confirmed Saussure's laryngeal hypothesis), Linear B, which corresponded pretty well with Proto-Greek, and Elder Futhark inscriptions which display a language between Proto-Germanic and Old Norse. It would also help with the homeland problem (though I won't ellaborate there, given the sensitive nature of the topic). There's a caveat, though, in that cuneiform wasn't attested until around 3200 BCE (at least as of now), but Neolithic European symbols, if writing (which is, by the way, a minority position), predate it by several millennia.
Borrowing from a previous answer of mine:
"Proto-Indo-European", as it's commonly used, doesn't refer to a specific, actual recorded language. Instead, it refers to a sort of hypothetical reconstruction. We know that various languages are related, and probably descend from a common ancestor; PIE is our attempt to reconstruct that common ancestor. To use a biological analogy, we know that humans and chimpanzees had a common ancestor at some point in the past, and there must have been, at some point, a last common ancestor. We can even try to reconstruct what that last common ancestor might have looked like. But finding fossils of that single specific ancestor is vanishingly unlikely.
What's more likely is that we'd find documents written in a previously-unknown Indo-European language, either written down much earlier than anything we already have, or having branched off from the others much earlier than anything else we currently know about. Or even both! And, in fact, this has happened in the past—when Bedřich Hrozný managed to decipher some cuneiform tablets in 1917, and showed that the language on those tablets was Indo-European. The "Anatolian" languages, as they're now known, were written down a millennium before any other other Indo-European languages, and also split off earlier than any other IE branch. And, even more startlingly, they showed evidence of phonemes that until then had been purely hypothetical, Saussure's coefficients sonantiques (now called "laryngeals").
Could something like that happen again? Absolutely! It's not likely, but it's plausible enough to build a story out of it. There are even several as-yet-undeciphered scripts out there in the world that might turn out to encode Indo-European languages. And evidence like that might completely rewrite the textbooks on Proto-Indo-European. It might not be PIE itself, but for story purposes the effect would be the same.
With some pretty significant caveats:
- Odds are extremely low that Linear A encodes any Indo-European language
- Odds are vanishingly low that any decipherable writing was produced 6750 years ago, since this is significantly earlier than any known linguistic writing
- Odds are impossibly low that it would be cuneiform, which wasn't invented until the mid-fourth millennium BCE
If you're using this as the basis for a work of fiction, I'd suggest putting the date significantly later, after the well-agreed-upon invention of writing. A connection to some other known writing system, like Egyptian hieroglyphs, Linear B, or cuneiform, would help quite a lot in the decipherment.
And note that we don't necessarily need older records to get a better picture of PIE: evidence from more distant relatives (but which are still definitely related) can help our reconstructions just as much, if not more! The reason Hittite and the other Anatolian languages are so important isn't because they were recorded so early, but because they diverged from the other Indo-European languages earlier than any other known branch, while still being recognizably related.