Indeed, and triremes were lightly built - from Wikipedia [1]: "Triremes required a great deal of upkeep in order to stay afloat, as references to the replacement of ropes, sails, rudders, oars and masts in the middle of campaigns suggest. They also would become waterlogged if left in the sea for too long. In order to prevent this from happening, ships would have to be pulled from the water during the night. The use of lightwoods meant that the ship could be carried ashore by as few as 140 men." Then there is the issue of provisioning hundreds of oarsmen. If a Greek transatlantic crossing was made at all, I would have thought a trading ship would have been much more suitable.

[1] https://en.wikipedia.org/wiki/Trireme