To emphasize the point: the Atlantic Ocean is roughly 3,000 miles from the Canary Islands to the Caribbean, or merely 2000 from Ireland to Newfoundland. Crossing the Atlantic means provisioning months of food and water, and being able to tackle navigation without any visible reference points. It also means being able to design ships that can handle stormy conditions, because you're likely to hit a storm in that time.

The first ships likely capable of making a crossing are the Chinese junks, followed by Polynesian outrigger canoes. The first European ships capable of making it are probably the Viking longships, which makes pre-Viking contact difficult to conceive, much less a sustained trading pattern. Furthermore, Phoenician ships were predominantly rowed, not sailed, which makes the journey especially hard to believe.