In the face of this objection:
We understand that God exists
We do not understand what God is/ his essence
Therefore, God’s existence is not his essence.
Existence (esse) means two things: either the act of the essence, or the composing of a proposition made by joining a predicate to a subject. Taking existence in the first sense, we cannot understand God’s existence nor his essence; but only in the second sense. We know that this proposition which we form about God when we say “God is,” is true; and this we know from his effects.
The point generalizes to the intellect or to any transphysical reality as such. To say that the objects exists, as Frege would put it, is not to say that we have an intuition* of it on which we can base a later discourse about their nature but to say that we can form true propositions about them by way of causal explanation. This is not at all the same thing as positing theoretical entities in physics, since the formal definition of these always involves some sensible thing like a reading on a gauge or a splatter-pattern on a photo plate. Unseen causes in physics are never formally unseen, though they do intimate the sort of causal explanations that ground metaphysics by not being seen in themselves but by proxies.
The absence of intuition of the metaphysical divides it formally from physics, and gives it an entirely different sense of evidence, proof, object, and claims to existence. The Naturalist demand for evidence or proof is almost certainly question-begging, since metaphysics does not claim to give one an intuition of the object either in itself or by some sensible proxy. That said, the Naturalist demand might be more charitably understood as a demand for the beatific vision.
*This is intuition as it was used from Ockham to Kant: the immediate presence- and so existence – of the object. It is certainly not “intuition” as used in Analytic philosophy, where it seems to mean an uninformed prejudice.