Seminole men traveled to Cuba to trade goods in dugout cypress canoes. If mainland Indians could cross the Florida Straits in the 18th and 19th centuries, there's no reason why they couldn't have done it in the 11th century as well.

The connections between the Lesser Antilles and Mainland South America appears to be much stronger though (Curent and Hauser 82).

I have a similar question. Did pre-Colombian Mesoamerican, or Andean civilizations have any sort of navies?

EDIT: added Pre-Colombian.