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To argue for or against it requires you argue using the methods of science.

Yes you can. Read the Philosophy of Science. If the scientific method used to develop the theory itself is flawed, all the conclusions are flawed. History is riddled with flawed scientific methodologies. If the concept of random mutation is not proven in the historical evidence, why should I have to believe it, because a bunch of scientists in the field do?

I can say science is good at things it can directly verify, and no good at things that happened a billion years ago. Scientists can say a meteorite caused dinosaur extinction and I can say BS: you were not there with quite a degree of confidence that I am correct. Science can be and is often misapplied.

The Nature and Philosophy of Science

If the concept of random mutation is not proven in the historical evidence, why should I have to believe it, because a bunch of scientists in the field do?

Because random mutation is not merely a concept. It is a fact established by 150 years of observation. Anyone finding a source of mutation that "looks ahead" and anticipates need will certainly be in the running for a Nobel Prize.

To argue for or against it requires you argue using the methods of science.
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Yes you can. Read the Philosophy of Science. If the scientific method used to develop the theory itself is flawed, all the conclusions are flawed. History is riddled with flawed scientific methodologies. If the concept of random mutation is not proven in the historical evidence, why should I have to believe it, because a bunch of scientists in the field do?
I can say science is good at things it can directly verify, and no good at things that happened a billion years ago. Scientists can say a meteorite caused dinosaur extinction and I can say BS: you were not there with quite a degree of confidence that I am correct. Science can be and is often misapplied.

The Nature and Philosophy of Science

Did you write that? It is unattributed.

In a scientific discussion, it is not very nice to refer people to an unattributed source as evidence. I usually like to know, for a start, who wrote something, what their biases might be, and then, if its worthwhile, spend some time with it.

So, did you write that? Or do you know who did?