No, those texts are about the time of the building of their own cities and civilization. The older big Sumerian cities are dated back between like 6000 and 3000 BCE (with Eridu around 5500 BCE). That's what the faraway days are.

The instructions of Shuruppak, the oldest known example of that line, is dated about 2600 BCE give or take, and it's talking about the city of Shuruppak and a king teaching his son Ziusudra. Ziusudra is later named as the Flood survivor in the Gilgamesh texts starting 2100 BCE, and the Flood in question is believed to point to one particular flood that destroyed Shuruppak around 2900 BCE (it got better).

The Sumerians of the Ur III period who wrote those texts (at least put them in writing from a probable older oral tradition) perfectly knew their civilization was old AF, more than a thousand years. The use of Ziusudra / Utnapishtim in the Flood narrative of Gilgamesh almost definitely points to the Instructions of Shuruppak, a text the later Sumerians and Babylonians also made copies of, being the specific "wisdom from the time before the Flood" that Gilgamesh brings back from meeting the guy. Like, they're saying Gilgamesh is the reason they all got copies of what Ziusudra's dad told him about how to make a city right - because Ziusudra repeated to Gilgamesh what his dad taught him (just before his city was wiped by the gods). It's also probably an explanation on why that specific line, "in those days, in those faraway days", is repeated in Gilgamesh, because it's in the Instructions. The "death of Gilgamesh" poem goes like this

you reached Zi-ud-sura in his dwelling place. Having brought down to the Land the divine powers of Sumer, which at that time were forgotten forever, the orders, and the rituals

And as a bonus, the Shuruppak flood would be around 2900, Gilgamesh would have lived around 2700, and the oldest copy of the Instructions is from around 2600, so even that timeline matches in their reconstruction if we imagine they figured that out correctly (or more realistically, Shuruppak was rebuilt after the flood destroyed it and that's when they wrote it themselves).

Proto Indo Europeans have no connection to them, no genetic, geographical, or cultural connection. They are probably a bit later than the older Sumerian cities, even.

Why would Akkadian or semite myths speak about a people that not only isn't theirs, but also unknown?