But it doesn't matter how much or little we know about the origins of our universe. No one's ever established that a creator deity is the only possible explanation. I think there's something very strange and counterintuitive underpinning our origins, if we even have an origin to speak of, but to call it "God" is what I consider most redundant.
Well as I elaborated above, I think you misunderstand my claim as well as possibly Prof. Hawking's claims too. Saying God is needed for the Big Bang is as unnecessary as saying Zeus is needed for lightning. Just because we haven't found an explanation, and possibly never will, doesn't mean that an explanation doesn't exist. So we can speculate based on what we observe in the here and now, and that speculation can include a deity if you like, but speculation is no substitute for fact.
No one has given a logical, causality-based explanation for our universe that includes God without running into logical paradoxes of their own, i.e. if God made the universe, then what created God? For Stephen Hawking's own part, I believe he is merely stating that there now exist theories which explain the known universe in its entirety, at all moments in its existence, provided you accept that certain natural laws have always existed. Doesn't mean these theories are correct or explain anything in a way human intuition could ever fully grasp, it just means we can now speculate on a mathematical level as well as on a philosophical or spiritual one, and plugging in a deity has never been of any practical use in this search.