The beginning of the universe is interesting. That time can begin is hard to wrap the mind around. Of course, the concept of time is something we humans have constructed and understand. I'm not sure we can really understand how our current conception of time can be applied to a hypothetical beginning of the universe. There is obviously immense uncertainty. So much uncertainty that I don't think there should be a null hypothesis regarding the beginning of the universe, if it even exists or if we could even frame it that way. I'm not an expert on physics nor theology for that matter, but I propose that there is no explanation that is strong enough to justify having it as "the best explanation." I don't think that saying a supernatural being began it all is convincing enough to warrant it being the best explanation.
Again, regarding the complexity evidence of DNA, just because something is complex does not mean that the simple "God did it" answer should hold sway. There are some things we cannot explain yet. That does not mean God did it.
Your protein and DNA argument is the same sort of deal.
I'm not sure if I'm understanding your eye argument correctly. Eyes provide an evolutionary advantage as seeing increases the chances of survival and can quicken reproduction. The mutation that led to the development of eyes proved beneficial.
Teleological argument: Can it not be that life occurred without God? There is likely life outside our planet as well given the immense size of the universe. With an unthinkable number of planets in the universe, surely some of those planets will meet the conditions for life. And our planet is one of them. This argument does not support the existence of gods.
None of my opponent's arguments are convincing enough to conclude that there is likely a God. Just because the Big Bang theory and evolution does not have all the answers does not mean God is automatically the answer to fall back on. It's a false dichotomy. So you don't think the Big Bang theory is valid. The God theory is no better. You say a supernatural entity created the universe. That is NOT the null hypothesis and that is NOT the best explanation. No explanation and uncertainty is better than an unsubstantiated explanation. I stand firm on my belief that there is no reason to believe gods exist.
1) Aposteriori evidence
1.1 Kalam Cosmological argument
1.2 DNA self-production
1.3 Irreducible Complexity
1.4 Teleological argument
2) Apriori evidence
2.1 Anselm's Ontological argument
2.2 Rebuttal of standard rebuttal of ontological argument
3) Aposteriori evidence
3.1 Mathematic impossibilities in the human population
3.2 Cosmological impossibilities
3.3 Biological impossibilities
1.1 Kalam Cosmological argument
My opponents premise against the Cosmological argument rests on the assumption that: 'a hypothetical beginning of the universe.' According to him, the start of the universe is hypothetical. If the start of the universe was hypothetical, then all life is hypothetical too, and nothing exists. We exist; therefore the start of the universe existed as much as we do. The base view shared in the scientific community is that the universe started. My opponent did nothing to refute this first cause argument, and thus it still stands. I would also like to point out some flawed reasoning by my opponent: 'I propose that there is no explanation that is strong enough to justify having it as "the best explanation."' It is the only explanation, and the reason why you won't find another is simply because science cannot deal with whatever cannot be observed or measure, thus no scientific theory can be asserted upon the beginning except for God.
My opponents attempt to refute misses the point. I argue that complexity is a reason to believe in God, my opponent says that it doesn't prove God. This argument still stands as a reason to believe in God.
DNA makes the protein that makes DNA, one cannot exist without the other and neither can work in any simpler state. There is no such thing as 'simple' DNA that makes 'simple' protein that can evolve. DNA is simply a collection of Base pairs that form an immensely complex code. Evolution cannot explain how it started. My opponent’s rebuttal is: 'Your protein and DNA argument is the same sort of deal.' So he is arguing that since nothing except God can explain it, then there is still no reason to believe God did it? Very flawed reasoning, this argument still stands.
1.3 Irreducible complexity
1.3.1 the eye.
My opponent conceded as to not comprehending my argument. The argument was that an intelligent force is required to mutate an organism into something vastly complex due to trial and error being a reason to wipe out a species. If an organism were to evolve but to do it incorrectly, as is often the case, it dies. That means that every life form on earth should be simple and not as complex, especially in light of the fact that complex organisms do not get much of an advantage in the first place. Charles Darwin said: "To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light and for the correction of spherical and chromatic aberration, could have been formed by natural selection seems, I freely confess, absurd in the highest degree." 
Evolution doesn't explain many things that not even humans can understand. Until we can make sense of this biological complexity, it remains a very good reason to assume it was created.
1.4 Teleological argument
the existence of the Fermi paradox refutes all my opponents’ claims that there should be an earth suitable for life. There should be millions. But the fact that earth is the only planet with intelligent life on it is a blow to evolution. Why isn't the universe swarming with intelligent creatures? According to evolution and my opponent, there should be. This argument still stands.
2.1 Anselm's Ontological argument
Refer to  if you do not understand logical symbolism.
2.2 Defence against the standard rebuttal
one of the most common attacks against this chain of logic is to create a reverse ontological argument. So instead of the chain reading God exists, substituting the premise 'it is possible that God does not exist' should in effect, cause the conclusion to read ‘God does not exist.’ But switching premise 2 with God does not necessarily exist causes a contradiction. Line 9 would become: God necessarily does not exist. So put simply, substituting for a reverse ontological argument causes premise 9 to state that a perfect being cannot possibly exist. But this falsifies a non-falsifiable definition. If a being is possible (e.g. the greatest possible being) it can’t be impossible. This Ontological argument therefore, stands in favour of God. It is more reasonable to assume his existence than his non-existence.
Gaunilo argued that this logic can be used to prove anything, like an island, of which no island can be greater, and thus, this perfect island exists in reality. There are a number of reasons why this is not the case:
1) the ontological argument can only be used to justify the existence of a greater 'thing.' Nothing specific, like an island.
2) There is no limit on how great an island can be, or something physical. It is like a number, there is no such thing as the greatest possible number.
3) Physical entities are subject to a different definition of perfect, and thus cannot fit the Ontological argument. A perfect God is a God that exists; a perfect island is one that has palm trees.
Conflicting evidence in evolution:
3.1 Mathematical impossibilities of human populace.
The human population doubles every 168 years approximately.  If the human race is 2 million years old, then the period of doubling should be 65,040 years. But wait! There is a solution. Since by this formula we appear to have a small bunch of humans in existence of their own about 5000 years ago, we can assume that there was a major catastrophe that killed everyone. I.e. a worldwide flood. This certainly points in God's favour.
3.2 Non-homogeneous universe
if the big band is true, then the universe should have evenly spaced out galaxies; this is not the case however. [4, 5] Most observable galaxies are in clumps bunched up together. How does the evolutionist explain? 'It's because of something that we can neither feel, see, smell, hear, taste nor detect using anything... dark energy.' Sounds like a religion hey? What’s wrong with God if you're going to believe in the supernatural anyways?
3.3 Mutations don't work
Experiments on fruit flies over 1500 generations to a human equivalent of 37 500 years concluded that if flies can't mutate properly, it’s likely that nothing can. The flies remained flies during the tests and only developed severe fatal flaws in their genes. [6, 7] This experiment yet against proves that the 2nd law of thermodynamics is correct when it states that entropy must increase.
I have given my opponent plenty of reason to believe that God is a safe assumption. Especially compared to the alternate hypothesis. I have included a video of an interview with famous atheist-turned-theist Anthony flew, and his reasons for believing he was wrong. My opponents reasoning has been completely refuted, none of his arguments stand, compared to all of mine, thanks for the debate, Vote Pro. http://www.youtube.com...#!
 The Origin of Species, Charles Darwin, J.M. Dent & Sons ltd, London, 1971, page 167.
 R. B. Tully, Astrophysics Journal 303:25-38 (1986).
 Unlocking the Mysteries of Creation (Volume 1) , Dennis R. Petersen, Christian Equippers Ministries, Calfornia, 1987, page 84. 5Hoyle on Evolution, Nature, vol. 294, 12 November 1981, p105.