What do we know? Ostensibly nothing. Prior to the advent of written music, any music would have been passed down by rote, and we have no way of even guessing what it would have sounded like before being passed down from mouth to ear over a thousand years or more. So many changes are possible in that time that it would be virtually impossible to extrapolate exactly what particular melodies would have sounded like.
That being said, there are so, so, so many more musical writing forms than just western classical notation. I'm going to link you to a previous response I made about other music notation styles from around the world. So there are lots of styles of music that have written traditions that date back centuries or more where we know for sure what they sounded like. There are also tons of varieties of folk styles of music that, while we don't know if they sounded exactly the same, have remained faithful in terms of instrumentation, style, and musical form over centuries.
Finally, to kind of answer your question in a roundabout way, I will make mention of a cool musical passage that has popped up in various musical settings for nearly a thousand years. It's from a plainchant (commonly, though incorrectly called Gregorian chant) called Dies Irae. It's attributed to a monk named Thomas of Celano ~1200 C.E., though that attribution is likely incorrect, and it's possible the origins are even earlier.
The original hymn sounds like this:
Now here are some of the places that it's been used since the middle ages:
Among hundreds of others.