...Which came from European immigration, not to mention the medical and agricultural revolutions. Not all Americans are descendants from those original 4,600.
According to this chronology:
http://www.nwcreation.net/biblechrono.html which counts the generations between creation and Noah, the flood occurred ~4,500 years ago, around 2500 BC. We're not really talking about "thousands of years" here - if this timeline is correct, they would have a few centuries at best.