Egyptians in the New World?

[Praefectusclassis]

Ancient sailors were indeed not necessarily afraid of open water, but you do have to bear in mind that the Med hardly feels like open water: you really have to try to be out of sight of all landmarks (Holden and Purcell's The corrupting sea has a very instructional map). Those areas would be avoided, unless the wind (generally northerly) made your course very predictable. Hence the grainships sailing straight from Italy for North Africa, but not vice versa.