I find it hard to see how this kind of voyage could be done with a trireme however in Hellenistic times they were building much larger ships like the Tesseraconter http://www.naval-encyclopedia.com/hellenistic-ships/ . Personally I don't discount the possibility that some Hellenistic ship reached North America but unless proven it is hard to accept all this. I have seen a lot of theories over the years mainly because of the Pytheas journey mentioned below but without evidence they are just theories.

PS: Who knows maybe I do have some ancient ancestry in Canada :)