I think it's amazing that the same people who believe rocks can be eternal believe that God cannot. Since entropy increases more or less constantly in a closed system and since the totality of the universe constitutes a closed system, then matter cannot be eternal because it is in a constant state of increasing entropy. Since matter/energy can neither be created or destroyed, only changed in form, then scientifically the universe could not have a beginning. Neither could it be eternal. That leaves two options.
1. The universe does not exist.
2, The universe was created by forces beyond our understanding, capable of superceding the laws of physics.
You can pretend that the universe just popped out of nothingness and came to be if you want to. Me? I need a little more rational explanation. I find it a lot easier to believe in God than in eternal rocks.
Your premises are flawed.
1. Matter can be created. It can also be destroyed. It is the sum total of matter and energy that remains constant. Remember e=mc^2? That details the relationship. A huge amount of energy can form a tiny bit of matter, and a tiny amount of matter can release a huge amount of energy.
2. The entire universe may or may not constitute a closed system. One of the current theories is that gravity is so weak because gravitons 'escape' to alternate universes or something. Do I pretend to fully understand it? No. It's way way WAY outside my field. But that does not mean it is false or to be ridiculed. It just may not be quite correct. HOw we'd go about proving it, again, I don't know.
3. Entropy does not only increase. Entropy can also stand still. Ever hear of the word isentropic? Various systems can exist at states of constant entropy. It doesn't always have to be increasing. As a matter of fact, there can theoretically be a point of maximum entropy where the energy to generate more (i.e. break down matter into energy in a way that would increase entropy) isn't available.
4. Entropy measures the usable energy in a system, not the matter.
One of your conclusions is also flawed. You stated
You leave out a possible result and display a false dichotomy in the answer.
1. The universe does not exist.
2. The universe was created by forces beyond our understanding but completely in tune with physical and natural laws as of yet undiscovered by science and unknown to mankind.
3. The universe was created by forces beyond our understanding capable of superceding the laws of physics.
You left out number 2. But it is indeed possible.
Therefore, with both flawed premises and a flawed conclusion, your argument is invalid.
Also, just because entropy decreases the USABLE energy in a system, it does not mean the energy is gone, or destroyed, or whatever.
Metherion