1: Spanish settlement in Florida started in 1560s.

2: English settlement at Newfoundland started in 1583.

3: English settlement at Roanoke started in 1585 and had failed by 1590.

4: English settlement at Jamestown started in 1607 and continued throughout 17th century.

So, the Mayflower pilgrims settling in Plymouth was not the first English settlement in North America, nor was it the beginning of English settlement in what became the United States. And of course, Spanish settlement in Florida (and Texas) began before English settlement.