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That's not what science has established. There are not billions and billions of coincidences at all. The development of life on earth could have happened no other way. Mutations are a fact of life, as is the process of beneficial mutations being more likely to continue on and less beneficial mutations being less likely to continue on. Once you put this into the proper context—4.7 billion years—the process isn't billions of coincidences but a very straightforward process.
Would you like me to follow through? I can show you how bacteria evolved to be more resistant to antibiotics using verifiable data showing the rates of resistance. There's a 2007 edition of Proceedings of the Royal Society B: Biological Sciences that demonstrates it beyond any doubt.
The problem with your axiom is that it assumes unless a person him or herself tests a thing, it cannot be known to them. This assumes systemic corruption in every science, which to me communicates massive intellectual dishonesty. But if you really do doubt something scientific, you can test it. The fact that every time I've tested something, it's been confirmed gives me good reason to trust it.
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