Sadly, it is impossible to know anything about oral traditions and belief systems of people who lived during any period that was significantly before writing. While oral tradition can be persistent, it also drifts in content and over space. The earliest written records often include hints at contemporary folklore, and by implication, we may have an opportunity to peer a bit further back into a foggy prehistory just before the documents were created, but this is at best an imperfect lens, and it cannot be used to look too far before writing.

Rock art and various other forms of prehistory remains hint at belief systems, but it is impossible to understand what was behind these artifacts. Archaeologists make guesses, but there is no way to know anything about that beliefs and legends in earlier prehistoric periods. And this is certainly true of Neanderthals as well, since they are entirely locked into a prehistoric past.

A time machine is our only hope. I don't have much hope!