sookie960:Can anyone give me some advice please?
I can only suggest that you carefully go through any type of papers (identifying him) that he might have left behind in Greece, to help track him down in Florida.
If you have any such documents, present them to your lawyer in your home country.
He or she should be able to guide further (example: If there is an International Treaty for Child Support Enforcement with your home country, etc.).
Off the top of my head, when your son reaches the age of 18, he MIGHT be granted a U.S. Greencard - solely based on the fact his father is a U.S. citizen, IF he can prove (via Birth Certificate, etc.)
If your goal is to immigrate to the U.S., then I can only suggest you start the legal process now. Be aware if your husband dosen't want to be found, you might face a long and costly search.
I'm not a lawyer. This is only my opinion /suggestion. Most Replys' are based on information provided by the "original post" (OP).