A huge problem. It makes any demonstration of “infinite” power completely impossible, since any test anyone could ask for could also be passed by some finite (vast, yet finite) entity. Clarke’s Law kicks in here.
(At worst, a monstrously powerful entity could simply stamp “belief” directly on to my brain by force.)
Actually, the more I think about it the non-believers would be most likely to figure if one or more is a fraud. Unless they’re struck down by lightning. But I think there should be a special pleading to use them as referees.
Can you prove it is the truth, or can you prove you are correct? There is no proof of a God, nor can you prove there isn’t. It is your belief in other humans that determines
how or what one believes.