#1, If there was no moment of origin of the universe, all light elements (specially hydrogen) would already have been burnt up in star nuclei and we should see no shining stars. As a rule, all stars die. If the universe has been forever, there should be no more live stars because there should have been no star fuel (hydrogen) left to burn up anymore.
#2, The galaxies are moving away from each other at unimaginable speeds. This is an observed fact, not a theory. If the universe has been forever, the distane between the galaxies should be near-infinite and we shouldn't have been able to observe any galaxy in the univer other than our own.
#3, There is a process known as "radioactive decay" in which some heavy elements gradually break down into smaller elements which are stable and don't decay further. We have lots of radioactive heavy elements still present in vast amounts in the universe (take for example uranium and plutonium found in large amounts on our own earth). If the universe has been since time infinite, all these heavy elements should already have decayed into stable elements and we should not have any uranium, plutonium etc anywhere in the universe.
Now to the debate of God's versus universe's eternity. As a rule, we have to take someone/something as eternal. The problem with the eternity of universe has been discussed in the above 3 points. Matter cannot be eternal because there are several processes acting on matter (fission and fusion being the two most important ones) which only go one-way. The question "If God created the universe then who created God?" appears logical, but in fact is illogical. Using the same faulty rationality, one could ask:
If Edison invented the light bulb, then who invented Edison?
If Sidney Sheldon wrote a novel, then who wrote Sidney Sheldon?
If Microsoft programmed Windows 8, then who programmed Microsoft?
The theme here is that we are made of matter, so we can raise questions about the origin of matter. The presumed creator's (God's) existence is one step above our existence so we cannot ask (or understand) any question about the origin of God. Here is the reason why:
We live in a universe made up of matter, energy, time and space. Assuming God created all these things then God himself would be an entity for whom there is no time or space and who is not made of matter. Can our minds grasp the idea of any such entity who exists beyond the time-space frame? Someone who exists, and yet is not made of matter. Can we claim to truly understand such an entity?
No, we cannot.
When we totally immerse ourselves in material existence then we start to believe we are simply material beings and lose the ability to see the unique divine spark in every human being. In this consciousness our world eventually becomes dead and meaningless.
Does the universe even have a size ?
I believe it is a men's size 7. But we are are expecting growth, so if you are buying clothes, keep your receipt.