I think that people's senses of the presence or reality of God or divine persons counts as evidence, but maybe not proof.
For example, certain dogs have a great sense of smell. If they smell a person's trace, it is evidence that the person was present. However, it's not full proof because the dog could be confused, could be smelling the person's stolen clothes without the person being ever present, etc.
Similarly, a person could believe and report that he is seeing a small pink elephant, and it is evidence that he is seeing one, even if you don't believe his report or find the existence of small pink elephants to be ridiculous.