The math is simple. First you compare observations with multiple models, you check every single observation to see if it's more consistent or better explained by one model or another.
That's not maths, that's pure subjectivity. Where's the maths?
Creation point at the big bang would be better explained by an influence or a first cause (vs. nothing).
You can't possibly conclude that, since you cannot test "nothing". Also, what is wrong with the concept of an infinite regression?
A fine tuned design is consistent with the claim of intelligent designer.
I have already explained that fine-tuning is nothing but a logical fallacy. What's more, literally ANY observation could be considered "consistent with the claim of an intelligent designer" because any formation can be explained with "It was designed that way".
Billions of theists/historical accounts indicate past events of proportional significance and would be consistent with the claim that God exists.
False. It wouldn't matter if every single human who ever lived believe absolutely in a God (even if they all believed in the same God), it still would mean absolutely nothing with regards to the likelihood or rationality of God's existence.
If more observations are more consistent with a model, then this model would be more probable.
False. Something being "consistent" doesn't render it more probable. It lends nothing to any probability. Especially when the claim is so vague (like the claim of God's existence) that it can be used to fit or explain ANY observation that can be made.
It's not about evidence or facts,
You finally say something correct.
it's about weighing probabilities.
Then please present the precise probability of God's existence and how you worked this out mathematically.
We tend to reject God, simply because his being is not understood to us but this is not an evidence against his existence.
This is demonstrably false. Studies show that humans tend towards explanations that
include a God, not
reject one, because "God did it" is an easier explanation than actually having to consider a more complex explanation, and humans are somewhat limited by our natural tendency towards apophenia and personification of things we don't quite understand.