So, what about these things?
Abiogenesis is the independent origination of life by proton flux from inanimate matter. The dust from which Adam was created.
Bacteria and Archaea are the simplest forms of life that existed on earth for billions of years, and would have continued to do so, except for the once-off chance of the two combining
just once ever and never again in the whole history of the earth to originate the first eukaryotic cell, complete immediately with ATP synthase and all modern cell functions -- which of course went on to evolve, etc.
There is of course no such thing as attaching odds of chance to a singular occurrence. But the original bacteria/archaea endobiosis enabling the evolution of advanced life on earth is so unlikely that it only happened once, and has never happened again since.
As a theist I have my own thoughts of course. I am not a scripture literalist and my own belief tends to be a symbiosis of religions and my own experience. I'm not a religious dogmatist. I look to divine first cause. But of course it is not possible to assume the universe had any interest in evolving to produce intelligent life, or whether it just flipped out that way.
As I said earlier, when I look at the Hubble space images of whirling galaxies and exploding supernova, and when I consider the astronomical complexity of just one single eukaroytic cell, or the tip-of-the-iceberg Standard Model of physics with its building-block particles and forces -- I have to believe there is a greater intelligence behind it all. I simply cannot believe that, in the absence of space aliens, man is the highest intelligence in the entire cosmos.
But I cannot prove it. And I do not have enough science to be able to contradict findings by experts with anything else essentially than, as you say: I no-like, so it's wrong, man ...
On the actual question of evolution by gene mutation I will have to do research. For a start it has to be established whether that
is what scientists assume, etc. At this stage I simply don't know enough to comment. I also apologise for not reading your OP thoroughly.