Kids will independently re-invent most of these in their first few years of life. Circle? Five circles? Hand outline? One line? Perpendicular lines? Multiple perpendicular lines? Spiral? Being passed down thousands of years is not the best explanation for them being found everywhere.
I'm not saying these symbols qualify as a language, but this argument against it does not hold up.
There is no such thing as a child developing "independently" in the sense that you are using it here, and anyone who would try would be rightfully sued for child abuse in most countries.
Even a child with prelingual deafness who is denied Sign language and access to Deaf culture (and I recommend looking up what terrible impact that has on such a child's development and quality of life), is still surrounded by human symbols from the day they open their eyes.
[0] https://en.m.wikipedia.org/wiki/Prelingual_deafness
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)