I wonder if it is faith. There is an Islamic philosopher called Ibn al-Arabi who argued that for him there was no point in proving the existence of God since He is just so obviously all around us. Here he was thinking of one of the beautiful names for God, al-Muhit, the omnipresent. Suppose someone says that the presence of God is so evident to him that it is like believing that today is Thursday, or that the hands I see banging away on the keys of my computer are my hands. As Wittgenstein says, these are not claims that really one needs evidence for.
Perhaps the same could be said for the knowledge that the world is infused with divinity?