Is there any physical evidence that the Garden of Eden ever existed?

No, there is no evidence that the Garden of Eden ever existed. In fact, an analysis of the biblical text shows that it could never have existed as a physical reality. The Book of Genesis identifies four rivers that went out of Eden, the Pishon, Gihon, Tigris, and Euphrates. Only the last two of which are clearly known to us, but the Gihon is described as being in Ethiopia, which is actually in another continent.

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Leon R. Kass (The Beginning of Wisdom: Reading Genesis) says that there can be no single terrestrial place that would serve as the common source of these four widely separated rivers. True, the Tigris and Euphrates Rivers do meet, but the lands the text associates with the first two rivers are clearly separated from the Tigris-Euphrates valley, the first to the north, the second to the south. This geographical impossibility tells us that the Garden of Eden was a purely mythical place.