Logic and facts are puny things when it comes to the question of existence. Human beings do not (and probably cannot) comprehend the essence of matter-energy — the stuff of which the universe and everything in it is made. The following observations are therefore on a conjectural plane with all such musings.
Universe = everything that exists anywhere, including other realms (multiverses), unconnected with “our” universe; parallel realities (many worlds); and other discrete assemblages of matter-energy in space-time.
God = hypothetical uncaused cause of the universe — a being or force whose power, knowledge, and degree of involvement in the shape of the universe and its events are matters of faith.
1. The universe simply exists without cause, has always existed, and will always exist unless it contains the seeds of its own destruction.
2. The universe simply exists without cause, but came into existence at a specific (if indeterminate) time, and may persist or not (see 1).
3. The universe is coterminous with God (a kind of monism), has always existed, and will always exist, though its essence and form may change.
4. God and the universe are eternal, but God exists apart from the universe and may change the essence and form of the universe.
5. God is eternal and exists apart from the universe; He brought the universe into existence at a finite time, and — in addition to changing its essence and form — may extinguish it at any time.
DISCUSSION OF THE POSSIBILITIES
The idea of an uncaused universe runs counter to human experience, which finds a cause for everything. This is true even for quantum fluctuations, which involve the movement of energy from state to state but do not change the total amount of energy in the universe. Possibilities 1 and 2 are therefore counterintuitive.
Possibility 3 is consistent with some strains of theism and animism, and it is hard to separate from possibility 4. If the universe is coterminous with God, then (presumably) God shapes His own essence and form, but that leaves open the related possibility of a God who can diminish Himself and eliminate His ability to further manipulate the universe. This seems unlikely.
Possibility 4 posits an eternal force or being which stands outside matter-energy-space-time and shapes it (initially and/or continuously, to some degree). The unappealing aspect of possibility 4 is the eternal coexistence of God and universe, which allows the universe to arise without cause.
This leads to possibility 5, which is the most appealing one. It enables causal relationships in the fabric of matter-energy-space-time, while explaining the creation of those things, in the first place, by an uncaused cause. That uncaused cause precedes the universe, which is the proper relationship if God is not “just” the universe or coexistent with it (possibilities 3 and 4). And if God stands apart as Creator, then God (almost certainly) possesses the power to extinguish His creation. Possibility 5, of course, is consistent with the Big Bang, though there may be more than one of them in the past and future of the universe.
For the while, I leave (as an exercise for myself and the reader) the question of God’s role in the initiation and evolution of the universe and its contents.
Existence of God (Wikipedia article, with links to external sources)
Universes, by John Leslie
The Bible (Douay-Rheims):
Book of Genesis
 In the beginning God created heaven, and earth.  And the earth was void and empty, and darkness was upon the face of the deep; and the spirit of God moved over the waters.  And God said: Be light made. And light was made.  And God saw the light that it was good; and he divided the light from the darkness.  And he called the light Day, and the darkness Night; and there was evening and morning one day.
 And God said: Let there be a firmament made amidst the waters: and let it divide the waters from the waters.  And God made a firmament, and divided the waters that were under the firmament, from those that were above the firmament, and it was so.  And God called the firmament, Heaven; and the evening and morning were the second day.  God also said: Let the waters that are under the heaven, be gathered together into one place: and let the dry land appear. And it was so done.  And God called the dry land, Earth; and the gathering together of the waters, he called Seas. And God saw that it was good….
Gospel According to Saint John
 In the beginning was the Word, and the Word was with God, and the Word was God.  The same was in the beginning with God.  All things were made by him: and without him was made nothing that was made.  In him was life, and the life was the light of men.  And the light shineth in darkness, and the darkness did not comprehend it….
Atheism, Religion, and Science
The Limits of Science
Three Perspectives on Life: A Parable
Beware of Irrational Atheism
The Creation Model
The Thing about Science
Evolution and Religion
Words of Caution for Scientific Dogmatists
Science, Evolution, Religion, and Liberty
The Legality of Teaching Intelligent Design
Science, Logic, and God
Capitalism, Liberty, and Christianity
Is “Nothing” Possible?
Debunking “Scientific Objectivity”
Science’s Anti-Scientific Bent
Science, Axioms, and Economics
The Big Bang and Atheism
The Universe . . . Four Possibilities
Einstein, Science, and God
Atheism, Religion, and Science Redux
Pascal’s Wager, Morality, and the State
Evolution as God?
The Greatest Mystery
What Is Truth?
The Improbability of Us
A Digression about Probability and Existence
More about Probability and Existence