Surely religions start with the embellishment of the life of a charismatic figure or minor historic event, which in turn is further embellished via second and third-hand transmission until it receives the status of historical truth.
Only in the vaguest sense. Often there is a historical figure all right, but it's the author of the story, not the character in the story.
E.g., take Mormonism. There is a historical figure in there all right, but it's the author Joseph Smith, not the characters in his book, such as Alma The Elder. There was no historical Alma The Elder, for example. Joseph Smith just made him up.
For other deities, we may not know the authors and moment when the story was made up, but we can be pretty sure that the characters can't be anything but made up.
E.g., Amaterasu is not just a deity of the sun, not an avatar of the sun, etc, she IS the sun. It's pretty hard to imagine, if you know anything about animism, how the heck at any point in history someone could have mistaken a real person for the sun, and how that wouldn't be a fundamental conflict in animism. The much more likely explanation is that, just like the rest of animism, they just attributed an intelligent 'soul' to a thing.
Additionally some mythological events are clearly allegorical of events that happened millennia after the myth about that deity started, so they couldn't have possibly been done by an actual person, even if you want to believe that the deity was based on one.
E.g., take the Egyptian Hathor and her drunken murderous rampage up and down the Nile.
For a start, Hathor is the sky. No really, even her name says so. It's not with the English "th", it's Hat-Hor: house of Horus (the eagle.) It's pretty damn hard to imagine any point in history where a real person was mistaken for the Sky. Honestly, how tripping balls would you have to be to think that that gal over there is the sky?
But to return to that event, we even know what earthly event it's an allegory for, and when that story was made up. It was about a bloody civil war, and they add the story to the mythos right after it.
So, long story short, turns out that people actually are very capable of making stuff up
