No Specific Discovery Date
It is impossible to say when the first manatee was discovered. Manatees have existed for millions of years, and humans have likely encountered them for millennia in coastal areas.
There was no single "discovery" moment. Ancient Greek and Roman writings mention manatees, and European explorers encountered them in the Americas and Caribbean during the 15th and 16th centuries.
Manatees have been part of human history and understanding for a very long time.