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It's been discovered that the universe is constantly expanding, which strongly supports the big bang theory. There's no such evidence for god.
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There are very few self-respecting scientists who still believe in the Big Bang.
There are also 11 instances in the bible where God is said to have "stretched" out the heavens. Some claim it to be a coincidence, but in my opinion that is a pretty significant statement. When I think of something being "stretched" I certainly get a visual sense of expansion.
The big question for your big bang theory would simply be: What the hell exploded?
The problem is, if you answer that question, you open yourself up to SO many new questions that all lead back to a creator of some kind.
Then you have the law of angular momentum which would have applied to that mythical spinning ball containing all the matter in the universe. Sadly for Big Bangers, that law is broken all over the place. Hell, even several of our neighboring planets aren't obeying that law. Entire
galaxies are spinning backwards!
The Big Bang Theory is dead as an explanation for universal genesis.
You can find a VERY extensive article debunking the Big Bang theory
here.