Back in 1920 Florida had smaller population than West Virginia. Nowadays it's the third most populous state in the US (ahead of New York)
At least part of the reason can directly be attributes to Henry Flagler. He was so instrumental to the fortune of Florida that people sometimes joke that the abbreviation for Florida ( Fla.) stands for Flagler. Flagler used to be a part of Standard Oil until he invested his wealth into railroads, specifically the Florida East Coast Railway. He had retired to Florida for a while to recuperate and found St. Augustine to hold a lot of potential for tourism, especialy for northeners during the cold season.
Flagler started by building a hotel (the Ponce de Leon). He found he had to build proper transportation infrastructure if there was ever any hope to create a tourism industry in a place most Americans regarded as a swampland. So he modernized the railroads and built even more tracks to serve his business interests.
Flagler initially wanted to end his construction in West Palm Beach but decided to push it all the way to Miami ( or rather what would eventually come to be known as Miami). During this time he would continue building resorts and donating to hospitals, schools and other curcial facilities along the way.
He eventually built the railway all the way to Key West, which was a highly ambitious engineering project. However, bad waves derailed the train and service to Key West had to be stopped. But it is that very railway line that serves as the foundation for the US Highay 1, connectinng Homestead to Key West.
So Henry Flagler was a key force in the creation of Florida, in changing people's perceptions of it as a backward swampland to a place people would like to retire to.
But it would be shortsighted to also preclude the effect of immigration from Cuba as well as the zero state taxes that would inevitably draw people to Florida for business.
If you want to read more on Flagler and the railroads, check out Last Train to paradise by Les Standiford from your library. It's a pretty engrossing read.