again, there is a difference (in my mind) between lacking faith and just out right denying reality. In a world where gods intervene (direct or indirect) regularly it seems it is almost crazy to NOT believe in the gods,DIVINE INTERVENTION
Beginning at 10th level, you can call on your deity to intervene on your behalf when your need is great.
Imploring your deity's aid requires you to use your action. Describe the assistance you seek, and roll percentile dice. If you roll a number equal to or lower than your cleric level, your deity intervenes. The DM chooses the nature of the intervention; the effect of any cleric spell or cleric domain spell would be appropriate.
If your deity intervenes, you can't use this feature again for 7 days. Otherwise, you can use it again after you finish a long rest.
At 20th level, your call for intervention succeeds automatically, no roll required.
High level 5e clerics call on their god for aid and something completely DM determined happens.
The default 5e setup seems to leave plenty of room for ambiguity from the mortal perspective.