The Spanish were the first Europeans to discover and explore Florida (Ponce de Leon in 1513).

They first established a colony in 1559 at Pensacola, but it was abandoned by 1561.

They founded a colony at St. Augustine in 1565 conquering in the same year a French (Huguenot) colony established a year earlier in Jacksonville (Fort Caroline).

The Spanish continued to settle (though never densely) and control Florida until 1763, when possession passed to the British in the Treaty of Paris.

The British ran Florida as two colonies, East Florida and West Florida, neither of which joined the 13 colonies to their North in the Revolution.

Spain entered the Revolution against Britain, and conquered and recovered Florida in the Treaty of Versailles in 1783.

Spain ceded Florida to the United States in 1819 in return for forgiveness of $5m in Spanish debts. (This caused some of the free blacks and Native Americans living in Florida to flee to Cuba or the Bahamas to avoid US rule.)

So, there has been an Hispanic population in Florida since 1565 (though generally not particularly "substantial"). Spanish (which I guess you have to call "Hispanic") were the original European settlers in Florida, and there have been Hispanics in Florida ever since.