Watson Brake, another archaeological site in Louisiana, is even older. It is considered the earliest mound complex in North America, dating back to 3500 BC.
If there is a connection between the Mississippian mound builders and the Mayans, I think it is more likely that there was sustained trade and cultural contact between the two groups, but one didn't birth the other. The transfer of ideas, beliefs, art, and tools through trade could explain the apparent similarities between the two cultures. They are after all, not very far apart.
I know those links are from Wikipedia, but Wiki is great for basic info gathering.