If Earth were flat, things wouldn't disappear over the horizon in the way they do. Aristotle proved Earth is round, but I'd be willing to bet that sailors and communities that lived on coastlines would have known this fact long beforehand.
It is quite common knowledge that the Moon is receding from the Earth at 38mm per year and is about 384 000 km distant.
Do the math.
That would make the separation between Earth and Moon about 10 billion years ago.
Not 4.5 billion years as is commonly regurgitated by the unthinking parrots of academia.
But then its all about popularity and status and little to do with logic itself, innit?
This presumes that the moon started touching the Earth with a constant rate of recession.
This is a faulty assumption.
Currently, the most common theory on the formation of the Earth & Moon is that a smaller
planet collided with the early Earth in a glancing blow, with the remains of that planetoid
becoming the moon. I don't think you can determine the age of either from the mechanics
of that event, but instead it's the reverse, dating rocks on both has lead to that scenario. https://en.wikipedia.org/wiki/Theia_(planet)