This question is supposed to be the be-all, end-all of questions that are supposed to trump all discussions against theism. Our inability to answer this question is supposed to show that theism and atheism have at least equivalent problems concerning origins.
However, the atheist position is much weaker. The atheist claims that everything, including the complexity and apparent design of the universe, arose from nothing, in a naturalistic fashion, where no such mechanism is observable or has been observed. It is claimed that this is the same position the theist is in: that the origins of God, from whom all complexity and design flows, is also a mystery.
But if our origins are naturalistic, it is wholly unexpected and unexplainable that the natural processes which gave rise to our universe are still wholly unknown and, even worse, unimaginable, whereas it is not unexpected that the God who is outside of and indeed the creator of this complex universe is not open to our scientific investigation. The atheist's position is born from the absurdity of a priori denial of God; the theist's view can be defended as a logical deduction from the staggering complexity of the creation, as described by Behe and others, that so far has resisted all naturalistic and scientific explanation, as the very laws of physics (and therefore chemistry) have been shown to work against chance formations of life's molecules in primordial soups and so on. The fact that some scientists insist otherwise does not make their view scientific; real science, not just dogmatic assertions, wishfull thinking, or irrational faith, must support their claims, and to date this is just not the case.
Moreover, the rational being must accept that even if we cannot explain God's origins, it matters only that he exists, and that he may or may not have revealed himself and his moral demands in some manner or other, and that our choices may have eternal consequences. Even if we posit, as some do, that God was once a man, or some sci-fi (or sci-non-fi) notion of how he came to be, the only thing that matters is which revelation of him can be trusted, if any. And if he claims that he is outside of time and was never a mere mortal, that is something we will have to investigate.
As to the objection that we cannot obey or worship or interact with a being we cannot fully apprehend, this is silliness. We do so throughout our lives, with people, especially as regards the opposite sex. We relate to people whose ultimate origins and internal workings we may not fully or even partially understand. We drive cars without fully knowing their origins or design or internal workings. We use MRIs without knowing the full picture of quantum mechanics. It is irresponsible to use similar ignorance as an excuse when approaching the subject of God and our eternal destinies.