Although detailed records do not exist, traditional historians and archaeologists believe that the Olmec succeeded in much the same way as their successors, the Aztec and Mayan. This region of what is now Mexico has quite fertile land, which would be ideal for various agricultural purposes. There is no reason to believe that the early people did not grow things like corn and beans on a regular basis. Palm trees and plenty of fish and other seafood would form the basis of their diet and much of their trade.
For example, although the space thought to have been used by the Olmec was quite small, they did have perfect access to prime northern fishing that the earliest Aztec would not claim for hundreds of years. Of course, that area of Mesoamerica was certainly not all that far from the oceans at any point. It is safe to say that all the groups that made this region of the world their home had a considerably ocean-based diet.