Not long ago, I presented a theory about how deja vu could prove that a personal and omniscient god exists. This theory does a little more, though.
If two-thirds of people experience deja vu, that means that essentially each person has either had a personal experience with God, or knows someone that has. Which essentially solve the problem of divine hiddenness. Because if every person either had a religious experience or knew someone that had, the problem of divine hiddenness is not a problem at all.