No. Rivers in the Great Basin of the United States don't, for example.
I did not know that about the great basin.
Great Basin - Wikipedia
I do know the garden was not in the U.S.
I do know the Ogallala Aquifer could run out.
Crisis on the High Plains: The Loss of America’s Largest Aquifer – the Ogallala | University of Denver Water Law Review at the Sturm College of Law
Where are the rivers from Garden of eden now.
Two of the rivers most would agree on.
Tigris and Euphrates
I would think God obscured the exact location,
but is somewhere in that general vacinity.
Where Are the Four Rivers that Come from Eden?
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Tigris; The river flows south from the mountains of southeastern Turkey through Iraq and empties into the Persian Gulf.
Euphrates; Originating in the Armenian Highlands (eastern Turkey), the Euphrates flows through Syria and Iraq to join the Tigris in the Shatt al-Arab, which empties into the Persian Gulf.
The Persian Gulf is connected to the Indian Ocean through the Strait of Hormuz.
The Euphrates River is later mentioned in G‑d’s promise to Abraham regarding the Land of Israel, and is used as one of the defining borders of the Promised Land
Any exact place before the flood is guessing.
The Fertile Crescent could have been the area of
earliest human civilizations just after the garden.
https://www.history.com/topics/pre-history/fertile-crescent
"The Fertile Crescent is the boomerang-shaped region of the Middle East that was home to some of the earliest human civilizations.
Also known as the “Cradle of Civilization,”