There were actually 2 locations, the first a peninsula at the eastern end of the Mediterranean. The inhabitants left after about a hundred years to take up residence in the second near present day Baghdad. The peninsula sank beneath the waters of the Mediterranean over a period of 4000 years about 32,000BC. The second garden finally exhausted it's potential about 10,000 years ago. The "sudden" appearance of the Sumerians was all that was left of the glory of those days.
There's much more history in that book that will clear up a lot of misinformation displayed on this site.