Ah yes, the matter of Greek belief in their religion. This is one of the more common threads that pop up, but if anyone would like to put in their contribution, they're more than welcome to do so! For the meantime, here are some previous answers that address this matter:

• u/UndercoverClassicist here covers belief in general;
• while u/mythoplokos and u/Astrogator here explore 'belief' and how it was done back then.