The God vs no God debate is irrelevant for numerous reasons. 
 
First, one of the core principles of religion and God is to live your life according to a set of rules to get into the good afterlife. So, why is a God and/or religion needed to tell you this? If an afterlife does exist, then by most religions standards living your life morally and without causing others harm (i.e. the Golden Rule type stuff) is required. Likewise, if there is not an afterlife, most would agree that you should live your life morally and without causing others harm. The sole difference is one group believes that in addition to the "Golden Rule" principle, you have to believe in a certain religion. 
 
Second, it does not matter if God created the universe or if it "just happened" as both situations have no bearing on your life. If a God did it, then they have been basically hands off since then. If it "just happened", then the universe doesn't care about you individually (or about anything at all since it just is and has no will/intelligence). Either way, your life is not going to be impacted by one or the other. 
 
Third, it does no benefit to the species to argue for one or the other. Regardless if there is a God or not, science is the only proven way to further our species. Without it, we wouldn't even be in the stone age (even if it wasn't modern scientific methods that got us there). We learned how to harness fire, grow crops, etc through observation and testing theories until we found the best one. Humans did not get to this point of progress through saying "God did it." So far, there is not any evidence that factually supports a God type being from getting pissed off about advancing our society. If this God did not want our society to advance to question him/her, then the being would not have allowed it to happen. Thus, it's irrelevant if God does or does not exist, as advancing our society from caveman days to today has not had any negative effects from God that can be proven to be his/her direct intervention. 
 
Fourth, either you believe that there is free will or that everything that has and will be is part of an ultimate "destiny" regardless of it being due to God or it "just is." If you believe in the free will side of this discussion, then you have the free will to believe or not believe in God. A God who gives a society/species free, and is a just God, cannot punish you for exercising your free will to believe what you want (even if those beliefs do not include him/her). If you believe that the universe is deterministic, and you have a destiny/fate, then your belief has already been determined as have your actions/inactions. That would mean your afterlife has already been determined as well since most religions having you going to the good/bad afterlife based on your actions/inactions during life which were already determined. 
 
So, arguing for/against God is as ultimately pointless as life in a universe that "just happened", since it does not benefit you or society as God is a matter of personal choice or has already been determined and you have no choice in your beliefs. Living your life to ensure that you live it to the best of your ability, and trying to leave the world in a better place than the one you came into is the best policy for either God or no God based beliefs. All beliefs are adaptable, even religious ones (Catholic church dogma has progressed from Earth-centric, flat Earth, etc to today where it accepts that the Earth is not flat, and the Sun is the center of this solar system). 
 
To answer the OP though, there are 3 options for how "time" works:
1: No beginning, no end. 
2: A beginning, but no end.
3: A beginning, and an end. 
 
All 3 of these depend on your perspective, and things that we as a species do not know yet. All 3 are equally valid depending on how you frame the arguement. The universe we currently live in does have a beginning, but if there are cycles/multiverse/strings/membrances then it could have existed forever and there is no way to know as we are bound (to the best of our knowledge) to this universe. It will either end through contracting and the "big crunch" type event (where there would be an end to the universe we live in) or it would end in heat death (where there would be no end to the universe, even if it is "dead/dark"). 
 
For me personally, based on everything I know, time "began" when this universe started (i.e. big bang) since information about anything prior to that was almost certainly lost. There is no imaginary clock that is ticking, time is relative to what you are discussing though because it is a human construct (just like math) to explain the world we live in.