geography - Rivers in Genesis

I will be upfront about it - I am skeptical of our tradition about the Torah being given on Mount Sinai, and suspect that Judaism is a man-made religion. It's not that I don't want Judaism to be true, I do. It's just that it seems to make claims about this world that are falsifiable, and that I consider to be falsified. So I am asking about one of those claims here, hoping that I will get some good answers.

The four rivers. In Genesis 2:10-14 we are told that a river emerged from the garden of Eden and then parted into four heads:

The name of the first is Pishon; it is that which compasses the whole land of Havilah, where there is gold... And the name of the second river is Gihon; it is that which compasses the whole land of Cush. And the name of the third river is Hiddekel; it is that which goes towards the east of Assyria. And the fourth river is Euphrates.

There is no river in the world that parts into the four rivers mentioned. Although we are not acquainted with any river called Pishon, we know that Gihon is only a small spring in Jerusalem. The Hiddekel (which is the Hebrew name of the Tigris river) and the Euphrates are not two "heads" splitting off of one major river; the opposite is true: at Al-Qurnah (Iraq) these two rivers join to form the Shatt al-Arab. Some Rabbinic commentators on the Scripture (Rashi and R' Saadiah Gaon, for example) interpreted the name Pishon as referring to the Nile, but then we have a serious problem: there is not, and never has been, any connection between the Nile and the Tigris or the Euphrates.

Does anyone have any idea how a river could have split into these rivers and there be no evidence of it today?

Answer

Does anyone have any idea...

So this is my own idea, and not based on a source, but in line with Baby Seal's comment:

Obviously the Garden was of quite a different fabric than the psychical world we live in. I imagine a gradual transition from spiritual to physical, where at some points the four rivers begin to appear physically (tiny springs etc.), remaining mostly spiritual, but slowly becoming more and more manifest (large rivers), only to eventually become wholly physical.

This would be similar to (or even an instance of) the ohr ein sof decending through the sfiros, eventually taking the form of our physical world in the sfira of malchus.

Being that the fully spiritual is beyond all limitations, location too, the physical distance between apparent starting points of the four rivers would not be problematic.