Any argument based on the observation of the physical world necessarily suffers from the p<.05 problem.
"Luck is inherent in random trials. In a medical study, some patients may be healthier. In an agricultural study, some soil may be more fertile. In an educational study, some students may be more motivated. Researchers consequently calculate the probability (the p-value) that the outcomes might happen by chance. A low p-value indicates that the results cannot easily be attributed to the luck of the draw.
How low? In the 1920s, the great British statistician Ronald Fisher said that he considered p-values below 5% to be persuasive and, so, 5% became the hurdle for the “statistically significant” certification needed for publication, funding and fame.
It is not a difficult hurdle. Suppose that a hapless researcher calculates the correlations among hundreds of variables, blissfully unawarethat the data are all, in fact, random numbers. On average, one out of 20 correlations will be statistically significant, even though every correlation is nothing more than coincidence.
Real researchers don’t correlate random numbers but, all too often, they correlate what are essentially randomly chosen variables. This haphazard search for statistical significance even has a name: data mining. As with random numbers, the correlation between randomly chosen, unrelated variables has a 5% chance of being fortuitously statistically significant. Data mining can be augmented by manipulating, pruning and otherwise torturing the data to get low p-values."
An observer within the universe has no way of knowing if he is observing random chance or intelligent design. Given enough variables, enough time and enough universes, it is absolutely possible to live in a universe that is random but appears designed. And since "time" is itself one of the variables that can mutate, there's no way of knowing what the probabilities are from inside the system.
If God were totally contained within the universe, then the laws of the universe could be used to test for God's existence. But God is not contained within the universe. Although He holds every part of the universe in existence from moment to moment, He exists completely apart from it. The laws of the universe cannot contain God. As His creation, the laws of the universe may contain traces of His Being, indications of His characteristics, but that is all.
An objection might be raised. Did not Godel mathematically prove the correctness of Anselm's argument for God's existence? Why, yes. Yes, he did. Godel demonstrated that Anselm's proof for the existence of God was VALID according to the laws of modal logic. Unfortunately, Godel did NOT prove that Anselm's argument was TRUE. To be fair, he can't. Proving something true is outside the bounds of logical proof. Logic can only show validity. And even so, Anselm's argument involved thought, "God is that which a greater cannot be conceived," and thus is not obviously bound within physical universal laws.
So, any argument that relies on the "intelligent design" of the universe to prove God's existence fails. In fact, such an argument MUST fail according to the tenets of Christianity. Persons are not known by proof, they are known by self-revelation. The persons of the Trinity are self-revealed (which is why the OT didn't know there was a Trinity – the Trinitarian Persons had not yet revealed the inner workings of the Godhead). God is certainly pure Logic, but He is, more importantly, Three Persons.
Personhood is the key to discovering God. Thomas was chastised not because he sought physical proof, but because he failed to believe his friends, the other ten surviving apostles. In the moments before the risen Christ appeared, Thomas was in the same boat the rest of us have been in for 2000 years – we have no physical evidence, all we have is trust in eyewitness testimony and trust in Christ's self-revelation. Faith is the evidence of things not seen, but what is the evidence that warrants faith? According to St. Paul, it is the Resurrection. If Christ is not risen from the dead then we are all dead in our sins. Thomas objected because the apostles had only an empty tomb and some hysterical stories. Technically, the apostles weren't even eyewitnesses to the Resurrection.
Remember, even the apostles were not present at the Resurrection, they didn't actually see the physical event. The only people who were even close to being actual "eyewitnesses" were the (Jewish or Roman) soldiers guarding the tomb. Oddly enough, their testimony is not directly recorded anywhere. We have hearsay testimony of what they told the elders and their own superiors, but we don't have any Scriptural letter or other direct account from any of those soldiers. Six hundred years after the event, historical accounts begin to tell us Longinus, the soldier with the spear, converted, but none of the soldiers guarding the tomb, that is, none of the men who were most likely to have actually seen some aspect of the Resurrection, none of them are said to have converted.
The Jewish objection to Jesus is that the Old Testament prophecies a Messiah, but not a Messiah who shows up twice (Christians are still waiting on the Messiah's return - Jews consider that very weird).
Faith is the evidence of things not seen, but what is the evidence for faith? According to St. Paul, the Resurrection is the evidence for Faith. If He is not risen from the dead, we are still in our sins, and the most foolish of men to boot. But, the Resurrection was not seen.
So, according to Scripture, the Resurrection is the evidence for Faith, and Faith is the evidence for the Resurrection. Which is circular logic, and does nothing to convince anyone who buys into Aristotelian logic.
As Thomas shows, Christian faith can use physical proof, but that physical proof will always be secondary to God's self-revelation. Because God is pure logic, we must use logic in our search for God. Our search through the physical universe allows us to observe the witness the universe makes to God's existence, but that, by itself can never be sufficient. The physical presence of Christ before the apostles was not sufficient. The apostles required Christ to explain what their senses perceived. And even among the apostles who witnessed the risen Christ, "the eleven disciples went to Galilee... when they saw him, they worshiped him; but some doubted." The testimonies of those who claim to have seen with their eyes and touched with their hands are the best eyewitness evidence we have, but even that is not truly sufficient, as both Thomas and the other unnamed "doubting" apostles demonstrated.
It wasn't the apostolic testimony of the Resurrection that ultimately brought Christian belief to the Roman Empire, it was the apostolic service to others, their willingness to feed the hungry, clothe the naked, rescue the abandoned, care for the sick, bury the dead. In the last analysis, we must remember that while God is pure logic, at His core, God is Love. Thus, ultimately, we find God not through physical perception, nor logical analytics, nor even through emotional experience, but only through the choice to serve persons. We meet Christ through each Christian's choice to Love. After all, if God is pure logic, and God is Love, then the only logical choice is Love. If you want evidence of God's existence, start there.