Granted, it's not the best explanation. But stone age people did pass things down thousands of years.

For instance, the Alta rock carvings site was used for about 5000 years. They added new ones for some 200 generations. They managed to avoid wiping out the older markings, they managed to avoid the entire place being covered with scribbles. They definitively preferred this site, not any random suitable site, for their petroglyph narrative, whatever it meant. If place-bound cultural continuity can be so strong, who's to say something like it can't have survived journeys too?

(But yes, petroglyphs clearly aren't a language as we know it)