Another sort of puzzle about God

The existence of God has often been invoked to answer very puzzling questions like: "How is is possible for this world to have come in to existence?", and, more generally, "How is it possible for anything to exist?" But, the answer fails to impress those who are bugged by such questions because it simply provokes a further question "How is it possible for God to come into existence/exist?"
     It is difficult to get purchase on such a question, and even theologians struggle, finding themselves resorting to dubious properties like 'necessary existence' which then have to be subjected to endless refinement in the face of even the mildest critical scrutiny.
     But, there is a related puzzle in the vicinity - one that it seems is rarely discussed: "How is it possible for God to actually have the incredible powers commonly attributed to such a being?"
Imagine God reflecting on these powers: "How did I get these?"
Presumably, God would not be satisfied with anything along the lines of "Because I just happen to have them" (that surely makes them contingent, if not arbitrary). And, "Because I have to have them" or "Because it is just in my nature to have them" would be opaque, and hence equally unsatisfactory.
    Presumably, God would have an answer (if the question makes sense). But, there seems to be no way we could ever understand it.
     Of course, this way of describing things projects a very human-like psychology onto God. But, absent that, it's not clear that we can ever gain any understanding of God (this suits some theologians, along with others who find the smokescreen of 'mysteriousness' rather handy), and, more importantly, it's even less clear that God can ever understand us (which, some might say, would explain a lot).