The critique of natural theology since Kant has been that God is not an object of possible experience. I think the claim involves a confusion of experience and sensation, and that experience is a more subtle concept that can include God, even apart from mystical or religious experience.
So says James Chastek  in a post entitled ‘What is Experience?’ It is an issue that comes up in spiritual direction and in training spiritual directors: How am I supposed to know how God is looking at me?
‘How is God looking at me? ‘ is such a characteristic question of Ignatian spirituality and spiritual direction and indeed it asks a lot of modern people because it so goes against the cultural grain.
Chastek distinguishes between sensation and experience:
It follows that “to experience an object” can either mean to encounter it (a) as a part of the sensation, or (b) as part of the ordering idea. In natural theology, no one encounters God as (a) – and theologians even give many proofs for why this cannot be done. But they insist that God is experienced as (b), as a creator, a guarantor of rationality, a primary agent, etc..
I like what he is doing but my own line would be more to appeal to the imaginative and spiritual senses for an analogy. Chastek’s (b) sounds a little too abstract for spiritual direction. Ignatius expected his ‘exercisers’ to have easy access to an imaginatively mediated encounter with God that would provoke all sorts of feelings and thoughts in them.
When someone in spiritual direction is able to answer the question ‘ how is God looking at you now?’ the answer is often very important to them, often because what they ‘see’ when they ‘look’ at God ‘looking’ at them is a surprise. And not a surprise in the sense of some new bit of information about God — it is more that God is revealing to me something personal — God’s own feelings, desires, heart.
It is that sense of surprise and revelation that cuts through the arguments against experience of God. For all the doubt that an encounter with God is possible all it takes is some patience and then the arguments are trumped by experience.