"How could such a structure possibly have evolved its way into existence one random mutation at a time?"
As I studied and practice medicine, this alone was enough to convince me that life and the universe could never had developed without a Creator of infinite or seemingly infinite intelligence.
My other experiences confirmed this conviction.
The probability of amino acids randomly combining to create even the simplest folding protein is about 10 to the negative 164th power. This is a number larger than all the molecules in the known universe.