One has to wonder why the ancient Egyptians or peoples of the ancient Mediterranean using improved Egyptian technology, like the Greeks and Romans, didn't reach America if those ships were capable of crossing the Atlantic.
Because, and this is the thing Thor Heyerdahl and his fans never think about, they had literally no reason to do so. Heyerdahl, even if he was using period technology, was using modern knowledge and preparation for a transoceanic voyage.
We'll say the storm is I dunno 20 hours long and they drift far off course and are unable given the currents to change direction.
I know it involved a lot of handwavium and appealing to extraordinary luck, and circumstantial fortune but it isn't impossible. Just a big storm the currents carrying the fleet westwards.
So they starve on the open ocean because they don't have enough provisions to cross the ocean and, having no idea where they are, waste time trying to get back home.
That's why I imagined a massive invasion of Hibernia or perhaps a quixotic and grandiose Roman emperor seeking to conquer Thule.
1. Why are they invading Ireland, and with so many men? Romans might've been a bloodthirsty lot but even they had to come up with good reasons for conquering places. Britain was a valuable target, Ireland was not. There's a reason that IOTL they never bothered.
2. Emperors, especially in the period concerned, never had that kind of power. A nutty, quixotic emperor willing to sign the death warrants of thousands of men to discover a land across the ocean that exists in his imagination is going to be part of the very large percentage of emperors that die violently. Probably at the hands of the army that finds out they're being sent west, if not the Praetorian Guard, those traditional slayers of emperors. Look at what happened to all the other "eccentric" emperors.