There is no logical problem with assuming indefinite existense of either God or existense. (I have intentionally avoided using the expression "material existense" as I believe that it is a subset of existense itself, which may or may not include a "supernatural" [non-material] existense.)
Since positing either that God always exists or the universe always exists leads to no logical contradiction, and either other premise that requires a "beginning" is either self-contradictory or requires a further supposition (of whatever preceded the hyopothetical beginning), one or the other must always exist, God or existense-without-God.
If you are a thorough-going naturalist, the answer is the univers always exists (in some form). If you are not convinced of the naturalist position, you better consider God.
(There is an intentional flaw in this argument. Do you see it?)
Hank
I'll take a stab at it. It is the subject of time itself. Since I see time as a part of creation, I see God as existing outside of time. That is why I don't interpret the concept of "eternity" as time unending but, rather, a place outside of time as we know it.
So when you say God or anything "always" existed, your really saying they have existed since time was created or your saying they simply exist - as God described himself as "before the heavens and Earth were, I Am." What an odd mixture of tense in a sentence. I think this is one of the most powerful statements in the entire Bible. Oh, and on a side note, Christ also claimed to be God when he said "I am the I am."
Anyway, trying to describe when things, or God began in a paradigm that assumes time is the one constant drastically limits the scope of the question. If the assumption is correct, fine. If it's wrong, then the question is nonsensical, like asking a single man, "is it true that you've stopped beating your wife?"
The whole problem, ultimately, is that we are the equivalent of chickens trying to figure out when the barn was built. Chicken Run notwithstanding, it is a waste for God to even try to explain it to us intellectually (the limited brain, that is, as opposed to the vastly superior spirit).