Well, according to LANDSAT satellite data, there is indeed a "fossil river" (now known as the Wadi Batin) that flows out of what we now know to be Saudi Arabia, and a dammed river ― the Karun ― which used to flow into the Persian Gulf from the Zagros Mountains in Iran. Ah, could these be the missing Pison and Gihon rivers? If the Wadi Batin is the Pison ("gold" definitely seems to be suggestive of the color of Saudi sands), then where's the Gihon at? The Hebrew word that for centuries has been mistranslated as "Ethopia" is really "Cush" or "Gush" in romanized form, and, wait, it appears to be a loanword from Sumerian, where "Kashshu" is the correct spelling. This leads us to a people known as the Kassites, who are hypothesized to have conquered Sumer/Babylon during the 15th century BC out of the east ― possibly right out of Iran's Zagros Mountains. Ah, now that would make the Karun River the biblical Gihon, wouldn't it? Now we're getting somewhere.
We have to take into account, however, that there was a time ― about 7000 BC ― when the Younger Dryas period went into effect (possibly caused by the air burst of a large object such as an asteroid or comet), literally reinstating the ice age for another millennium or two. The result? The sea level was a good 400 feet lower than it is today, and glaciers would have been able to form at much lower altitudes, such as in the Zagros Mountains and in the highlands of northern Saudi Arabia, the melting of which would have fed the rivers in question. So, with the low sea level in mind, we come to our next question: just how shallow is the Persian Gulf?
The answer: VERY shallow, according to some data I was able to find... if the data is correct, the entire Persian Gulf is on one giant continental shelf, which would make it only about 200 feet deep at the most. That means... Yup, the Persian Gulf was at one point a fertile valley fed by glacial melt. Then again, oh, yeah, its floor is a VERY flat floodplain. When the sea level rose rapidly as the glaciers began to quickly recede when the last remnants of the Ice Age ended (about 6000 BC), it reached a critical point where it could just push its way across the entire plain in the same kind of free reign that tides can freely cross the Bay of Fundy today. The result, of course, is just that ― a flood, taking the form of what would appear to be a massive tidal bore as the fast-flowing melt-river is shoving itself against the seawater that it's contributing to the rise of, which would have quickly overwhelmed what was once the earthly paradise:
So, yup, there you have it. What was once the garden of Eden is now the bottom of the Persian Gulf... ah, and it's definitely not a garden anymore, now is it? The water would have been flooding the area about as quickly as it flooded the Black Sea (only not across a natural dam like the Bosporus but rather through a narrow strait ― the Strait of Hormuz ― that would have channeled the rising seawater to an unusually high amplitude as it pushed against the outgoing glacial melt), forcing the inhabitants to flee to higher ground and/or inland. Alright, that's two events down; you thirsty for more?!