The only way it would be barely possible would be with the following scenario.
A Carthaginian ship, enroute to the Canary Islands is blown off course and discovers the Azores. Because of their climate a small settlement is founded. Gradually over the years, as more ships sail to the Azores, another ship is blown westwards to the coast of Brazil.
That ship, laden with goods for the Azores trades with the local indians, say on Marajo Island. By luck or good fortune it makes it back to the Azores, the Canaries or North Africa with rich goods it traded from the Marajo Indians.
At that point, small groups of very adventurous traders would start crossing the Atlantic to trade for the riches of the Americas. Over time, trading settlements would be created. It's not really colonizing the new world, but then, for the Carthaginians, the Punic, or the Greeks its just too far away for any serious colonization. It might however, provide the bitter pill that would innoculate the natives against European diseases.
Whether or not the Romans would visit these trading posts is debatable, however, even if they did, they also would have no reason to attempt to colonize the area.
There really isn't much chance of it happening, but it is just possible.