All of the rivers existed but after Noah's flood the entire world was changed. The plates moved around and the geography became entirely different. The fact that there are rivers called Tigris and Euphrates does not indicate that they are the same rivers and they could not have been because the entire world was deluged with water and I would guess all kinds of other things like volcanoes earthquakes and other natural disruptions occured. These events created the rock layers and the fossils that we find - just like how rock layers and fossils are formed in a matter of hours during a volcanic eruptions such as that of Mount St. Helens back in 1980 which you can study for yourself. All the rivers at one time existed but the world as it was known is no longer.
