Herodotus gives us three important reasons to believe it happened: 1) he tells us that Africa is surrounded by water except at Sinai -- how would he know this if the trip hadn't happened? 2) he tells us the sailors saw the Sun to their North when South of the equator -- how would he know this if they hadn't at least gone that far?! (well, he could have posited it had he known the Earth is round, but then he'd probably have told us that too) 3) he tells us how long the voyage took and that the sailors had to grow their own food, which tells us how large Africa was and is (though I can't judge if three years was enough given their technology) -- how would he have known that Africa was that large?!

Three correct details (Africa mostly surrounded by waters, Africa straddling the equator, Africa being very large) that would have been hard to make up out of sheer fantasy. Especially (2).

Though the Egyptians almost certainly long had known by then that the Earth is round and it's possible that he made very educated guesses and told us a fantasy just cause, and pretended to not believe the bit about the Sun just to make his story more mythical to his contemporaries. But is that likely? Did he do a lot of that?