The universe and brain are very complex, they need the existance of the Creator (God).
Yes, I believe that science can prove the existence of God in at least two ways.
One is that science has established with certainty the origin of the universe. The Borde-Guth-Vilenkin Theorem, proven in 2003, showed that any universe which is, on average, expanding throughout its history cannot be eternal in the past but must have a past space-time boundary. Since all mathematically and physically tenable models of the universe to date feature, on average, expanding universes, the universe must have a beginning. But then one can argue:
Since the universe is all time, space, matter, and energy, the cause of the universe must transcend these features. The cause must be timeless, because it brought time into being. Since the cause brought space and matter into being, it must be immaterial rather than physical. As the origin of energy, this cause must be enormously powerful. Such a timeless, immaterial, and enormously powerful cause is the core of what most people mean by "God."
Second is that scientists has established with certainty the fine-tuning of the universe for life of any kind. If the universe did not have precisely the right laws, constants, and quantities, then the universe would be life-prohibiting rather than life-permitting. The universe did not have to possess the laws, constants, and quantities it does. Moreover, it is vastly more probable that the universe should be life-prohibiting than life-permitting. For example, if the force of gravity were altered by 1 part in 1060, life of any kind could not exist. If the rate of the universe's expansion were altered by 1 part in 10120, life of any kind could not exist. If the initial distribution of mass-energy in the Big Bang were altered by 1 part in 10 to the power of 10123, the universe would not be life-permitting. One can then argue:
This verifies an intelligent designer of the cosmos, which is what minimally everyone means by "God."
I'm afraid your final proposition can equally point to existence as accident or one permutation amongst many, all possible and all probable. Had all this fine-tuning not occurred, nothing would have. But it may as likely occur in other ways and some other reality be dominant. Equally, the design we believe we detect in the environment may simply be evidence of our specific understanding, brain selection in effect, and may only be real on a number of levels, not all.
Case of science trying to prove the existence of God is like a salt doll trying to find the depth of an ocean. Moment the doll entered the ocean, it dissolved in the ocean. Now who is there to tell others how deep the ocean is?
https://www.researchgate.net/publication/266618399_Unified_field_of_consciousness
http://www.amazon.co.uk/The-Big-Bang-Assumptions-Problems/dp/1613245777/ref=sr_1_5?s=books&ie=UTF8&qid=1333360764&sr=1-5
Article Unified field of consciousness
Complexity, by itself, is a poor reason to invoke a creator.
One can (it is thought) with little more than gravity, time, and a collection of hydrogen, generate entire galaxies replete with 'complex' star and planetary systems.
I am aware of the anthropic principles that have been discussed in the literature (Barrow and Tipler) but I cleave to the notion that science cannot prove anything to be true. It can only either show that a model predicts the outcome of falsifiable tests, or show that a hypothesis is false.
Proofs of correctness are left to mathematicians.
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