One of the better attested non-Indo-European written languages, which alas, has not survived, is the language used by the Minoans of Crete. We have considerable historical or proto-historical information about their fall to the Mycenaean modern Greeks who are the linguistic direct ancestors of the modern Greeks. Indeed, Mycenaean Greek is one of the oldest Indo-European languages attested in writing.
The Minoans overlapped historically with the Sumerians, who inventing writing first. And, we have a fair number of examples of Minoan writing, although the written language appears to have been confined largely to professional scribes rather than being used by the general population, and seems to have been used mostly to keep bureaucratic accounting type records, for example, documenting taxes and welfare payments from the palaces that dominated that society. There are some prayers sprinkled in amongst the bookkeeping, but there are probably no great Minoan literary epics or histories reduced to writing in the Minoan system out there to be found. It was a step beyond a mere written proto-language system of symbols (which some have suggested is all that the Harappans and early Vinca script consist of), but only at the narrowest level. The share of Minoans who could understand it might be comparable to the share of modern Americans who could make sense of the equations in a physics journal article, or read and write computer code in its raw form.
No one has fully deciphered Minoan writing. But, a central element of what is left of Minoan writing is its system of numbers and quantity units, and Andras Zeke, the proprietor of the Minoan language blog, has offered up a quite convincing post that offers a comprehensive description of this key part of the Minoan written language. It is worth a look if you are interested in this kind of thing.