That's not quite true. The notion that nonbelief constitutes a grave insult to the god is rather modern by itself and comes from monotheism. (Furthermore, the notion that
insulting the gods, even your own patron gods, is at all
bad is not universal - for example, the polytheistic tribes of what is now western Russia though it a normal thing to flog your own idols or stick them into a latrine if they weren't helping out with the harvest / war / childbirth.
Destroying the idols and thereby murdering the gods, however, was genocide and warranted capital punishment.)
Nonbelief was punished when it got into the public, political sphere. Some officials were also priests, and, vice versa, temples performed public functions and were corporate economic powerhouses. Cities and monarchs traced their histories from gods and heroes. If you were walking around saying "Venus doesn't exist", you'd be basically calling the Roman emperor a lying mongrel bastard. If you refused to acknowledge Juno, you couldn't get married to a Roman citizen (but if you brought in a foreign woman and said you married her in Tyre, no one would object).
Could an atheist have prospered in antiquity? Yes, and many did, as long as they paid taxes and didn't go out of their way to insult local authorities and potential trading partners. The golden age of Carthage was a good time.
They actually were, there's a whole Wikipedia article.