An interesting point, is the generally accepted view of the re/discovery of Brazil by Pedro Cabral. He was on his way around the Cape, but sort to avoid the calms off West Africa, and catch the trade winds further west; a proven speedier method. But basically, they blew him a bit further west than he intended, and Brazil was found...

The fleet of thirteen ships left Lisbon on 9 March 1500, and following the course laid down, sought to avoid the calms off the coast of Gulf of Guinea. On leaving the Cape Verde Islands, where Luís Pires was forced by a storm to return to Lisbon, they sailed in a decidedly southwesterly direction. On 21 April a mountain was visible, to which the name of Monte Pascoal was given; on 22 April Cabral landed on the coast of Brazil, and on 25 April the entire fleet sailed into the harbor called Porto Seguro.
Now, I know Phoenician sailors (and virtually all sailors) of that time period, were loathe to leave the coast, but just maybe, some followed that route by accident.

And then who knows? On a side note, some Marine Archaeology friends of mine have been exploring the Bimini area for some years now. They are quite convinced, that they have found remains of what seem to be Phoenician type harbors in the shallow waters there..

I remain a sceptic with an open mind