Okay, you went back to Buddhism, older than the other two you mention, so that's 500 BC approximately.
Pythagoras and Confucius very roughly the same time. Jainism also the same time as the Buddha. Mayan religion is 750 years later (Mayan religion).
Modern Hinduism roughly contemporary with Budhism and Jainism, but gradually developing, not got a single founding figure, continuous with the Vedantic religions, so hard to say when it started exactly. But lets say very roughly the same time, so we can go back to before them too.
So you are talking about a time before any of those.
In India Buddhism is preceded by the Vedantic religions - which didn't yet have the idea of rebirth or the cycle of Samsara until shortly before the time of the Buddha. Oldest sacred texts in the world, preserved by brahmins who trained in memorization from a young age in order to preserve the texts in a culture without writing.
Then, you have shamanistic religions certainly. And Animistic -believing that there are many spirits in nature.
Including the Druids in Europe, and the American Indian religion in the States.
Then separate again, the Aboriginal religion, their idea of dream time.
Then, ancestor worship, common in Africa for instance.
Taoism based on ideas of balance and Ying and Yang
Judaism of course, idea of commandments from a single deity.
The Greek Gods, polytheistic.
Ancient Egyptian religion with their ideas of afterlife and the pyramids and again, many deities.
Sumerian religion which introduced early versions of many of the stories in the old testament.
That's just a few - enough to show that there were quite a few major religions already at that point.
I'm sure there were many more, those are just a few that come to mind right away.
She also mentions the Viking Religion - about which we can't say much except ancient stories, details lost in the mists of time, a bit like the Druid religion.
Incidentally the modern Bon in Tibet say that their religion - which has many resemblances to Buddhism - derives from a Buddha who lived 18,000 years ago. (Of course, could just be that it adopted many features of Buddhism when it was introduced to Tibet, and back dated their history after that to a previous Buddha).
Buddha himself also taught about the lives of previous Buddhas who lived thousands of years before him who taught the same teachings that he did. Well at least, sutras attributed to him say this. Traditionally he is the fourth of a thousand Buddhas. So that would take you back right back to the early paleolithic period if it was correct.
But there is no archaeological or other evidence of this to back it up. Which doesn't mean it is impossible of course.
So what can you do, when there is no evidence for these things?
Well, we can't say much at all about early religions before the invention of writing - unless they were memorized and handed down by memory.
The invention of writing is uneven. India for instance didn't have it until a century or so after the Buddha, around 300 BC. While Sumeria, not that far away, already had writing at 3000 BC
So we know a fair bit about the Sumerian religion because they already had writing, which we can also decipher. We don't know anything, hardly, about the religions of the similarly ancient Indus valley civilization because they didn't have writing - well they had what may be a script but we can't decipher it and it may not even be a script.
I think that there may have been complex religions way back to early paleolithic times. But we have no idea what they are. Especially given the diversity of the religions we know about.
Back then all we have are enigmatic figures and paintings or drawings which may or may not have had religious significance.
We can only guess what these meant to those who carved them.
Cup and ring marks, common in ancient stones in the UK and other places
Could be a form of writing, maybe even just saying something mundane such as recording a transaction, or maybe like a pub sign, not really a form of writing. But could also be of religious significance. Some attempts have been made to try to derive details of the Indus valley civilization religion from some of these seals, not very convincingly.
The Venus of Willendorf. We have no idea what these symbolized. Perhaps a fertility figure? Earth goddess? Can but guess.
Animals and what seem like doodles to us, in Lascaux cave. But for all we know they might have had a profound significance to the original artist, which is now lost.
Strong aesthetic sense, sense of balance and space and also great use of the shape of the stone itself in some of the paintings. We can respond to that but can't know what they originally evoked in the artist and the first people who saw them.
I think it is fascinating, you look at these art works, and in a way you have an immediate connection to the painter, in some ways the Lascaux paintings for instance, they could have been painted yesterday, they are so fresh looking. And yet, we have absolutely no idea what they were thinking, what they had on their mind when they made these images and figures.