One common objection to the existence of God can summarised as follows,
God, if he exists at all, is the most complex conceivable being; therefore, to postulate God to explain the universe, life or consciousness is by definition to postulate an explanation more complex than whatever it is you are trying to explain. And this leaves us with the more difficult task of explaining the explanation.
The objection (which is reducible to the schoolyard teaser, “Who created God?”) should be familiar to readers of Richard Dawkins’ book The God Delusion in which it is presented as the central argument against the existence of God. 
Three things need to be said in response to it.
The first is that a key premise hangs on the assumption that mental states are reducible to physical brain states and that the existence of an infinite intelligence therefore implies the existence of an infinitely complex physical substrate—analogous to an infinite computer or human brain.  However, when the theist postulates the existence of God he postulates the existence of an immaterial Spirit and so, ex hypothesi, an entity which lacks the “heterogeneity of parts” Dawkins himself recommends as the indicator of complexity. William Lane Craig suggests that the error behind this objection consists in conflating the mind itself with the mind’s ideas. “A divine mind may certainly have complex ideas,” Craig concedes. “It may be thinking, for instance, of the infinitesimal calculus while monitoring and controlling the status of every elementary particle in the universe.” But being unembodied it lacks physical parts and so is not complex in the sense that is required for Dawkins’ objection.
The second point that needs to be made in response to the demand for an “explanation of the explanation” is that the same demand can be made of any final theory of the universe. In scaling up the ladder of metaphysical explanation, atheist and theist alike arrive at a final rung. There will be, for both, a final brute fact or “explanatory terminus” for which there can be no further explanation. Physicalism, for instance, is the claim that only the physical universe exists. “The universe,” Bertrand Russell asserted, “just is.” But this is every bit as much a metaphysical claim as theism. And so the atheist cannot simply dismiss theistic proofs and rest his case; he needs to make his case in the court of philosophical analysis. There, our task will be to determine which of several competing explanatory termini (including theism and atheism) is on balance the most coherent given the total evidence. But demanding an “explanation of the explanation” is not a legitimate response to any final metaphysic under consideration because it leads to an infinite regress—we can then demand an explanation of the explanation-of-the-explanation; and then an explanation of that—and so on ad infinitum. In order to recognise that some final explanation is the best of several competing final explanations, it is not necessary or coherent to have to explain that “final” explanation by means of some further explanation. 
The third, final and most important point is that the question, “Who created God?” makes a category mistake. In postulating the existence of God the theist is postulating an uncaused and eternal being; that is, a being that exists in and of itself—a property theologians call “aseity.” Asking, “What caused the uncaused?” is akin to asking, “Who is the bachelor’s wife?” Nor does defining God as uncaused insulate theism against rational critique. The atheist can object that the concept of God is incoherent or that there is no evidence to support his existence. But what the atheist cannot do is dismiss the concept of an uncaused being a priori because the theist is unable to tell him what caused it. Uncaused entities are not incoherent in principle; on the contrary, they are a recognized concept in both philosophy and mathematics.  And critically, the atheist himself is postulating an uncaused entity in asserting that the physical is all that there is. When Bertrand Russell asserts that the universe “just is” he is asserting that the universe exists as a brute fact without cause or explanation. The question we must ask is which brute fact, the universe or God, is an inference to the best explanation from the philosophical and scientific evidence. And this is not resolved by pressing an objection against the theist that applies with equal force to the atheist.
 Dawkins calls it, rather clumsily, “the Ultimate Boeing 747 Gambit.” See Chapter 4 of The God Delusion.
 For a careful refutation of this assumption see, Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False by the eminent philosopher of mind Thomas Nagel.
 To illustrate this elementary precept of scientific reasoning, William Lane Craig invites us to imagine a group of archeologists who unearth artifacts resembling jewellery, pottery shards and arrowheads. They would be justified, he points out, in inferring that these object were the products of some unknown group of people rather than the result of the chance processes of sedimentation. And the fact that the archeologists cannot tell us who these unknown people were or how the artifacts came to be there in no way invalidates their explanation.
 As John Lennox, Oxford professor of mathematics, puts it: “The set of the uncaused in not empty.” It is rationally permissible to suppose that it includes mathematical and logical truths, moral values and metaphysical universals.