From what I've read so far, it would appear that the first trans-Atlantic seafarers were drug runners for the Pharohs.
An interesting theory.
Recently tests were run on ancient Egyptian mummies, that came up with astounding results. Evidence of their use of cocaine and nicotine showed up - in spite of the fact these are New World products! While some scholars are saying this must be from some African plants that were similar but now extinct (doubtful, but possible. One plant of particular interest was the "Silphium" plant, which was cultivated in what is now modern Cyrenaica in Libya - the plant was esteemed for many uses including medicinal and food. The plant seems to have gone extinct about the time of the Roman conquest of the area.) Silphium closely resembles the Anise plant (the licorice flavor) so may have been related. According to accepted history, China was not known to the west until the Roman empire yet genuine silk threads have been found on ancient Egyptian mummies too - proving that contact was more far reaching and far older than previously thought.
The more likely scenario is that there was indeed contact between the old world and the new which involved trade. In my opinion the Egyptians were not particularly good seamen, but the Phoenicians were! The trade routes they used were jealously guarded secrets, and their ability to navigate was well known. When the mother land was conquered, first by Babylonians and later by Persians and Greeks, most of the trading colonies became allied with Carthage. Carthaginian traders were quick to duplicate the navigational feats of their forefathers and to fill the void in providing trade goods. Thor Heyerdahl's famous "Ra Expeditions" proved that cross oceanic travel was possible even with the reed boats of Egypt, but navigation without compass would have been difficult.
It can be argued that the Egyptians had some method of using the stars for navigation, as the near perfect alignments of the pyramids could attest. However, it is my opinion that the Sphinx and certain other monuments ascribed to the Egyptians are in fact much older (circa 10000 years.) Egyptians did venture on the seas to the "mythical" land of Punt, a place which can be identified with Sumatra though theories abound as to its location including the Great Lakes of North America. A point to consider here is found in one of the ancient Egyptian inscriptions describing the expedition of Queen Hatshepsut to Punt - part of the text states "...the Phoenicians..." but the remainder of the text is missing. It is in a part of the text which is supposed to be a statement by the King of Punt, pointing out the secret path to the land and mentioning the "steps of Myrrh". The Puntese already knew of the Phoenicians by this early date, and to go a step further the Puntese were also called Puoeni by the Egyptians, which is a term also used to describe Phoenicians. The Puntese were most likely Phoenician colonists.
The Phoenicians were known to navigate by the stars, and in fact the Romans called the North star the "Punic Star" because of its use by them for navigation, but did not understand how. Another navigation tool called the "gnomon" was used to determine the latitude by the position of the Sun. A Greek sea-captain from Massilia (now Marsielles in France) named Pytheas learned the use of it and used it in his exploration of the Atlantic coast of Europe, noting that the Northern Star is not precisely at the North Pole as well as other remarkable scientific observations including the midnight sun at high latitudes and fog banks. On his return to Massilia, Pytheas was rewarded by his Greek fellow citizens with ridicule and scorn, an attitude that persists to this day among some scholars.
Another navigational instrument which probably was in use by Phoenicians was the cross-staff, a long sighting staff with uprights set at various spots which allowed the user to determine latitude as well as direction. Furthermore, some instinctive oceanic navigation skill was very probable among these sailors - similar to the unerring way Polynesians could find their way to tiny specks of land in the vast expanse of the Pacific simply by observing the formations of clouds, the flights of birds and even the way waves form far from land. A short passage from the Greek book "Argonautica" describing the man who was to be the navigator for the fictional voyage - as being able to judge the time for sailing by the wind and the sky, and the direction to land by the swell of the sea.