Good point on DNA. I would argue that the OP's initial idea may not have an answer due to lack of evidence.
What has occurred is reproduction producing similarities (common ancestry) is a more easily observed process and has thus garnered undue influence in the thinking of evolutionists, for lack of a better term, eager to prove their theories absent the data really sufficient to make good assertations. The process has thus been tainted.
There is overwhelming evidence for design, and the fact evolution is not really random, but totally governed by a number of factors. Mutations are not random. DNA displays some convergent tendencies for instance, and the principles of chemistry and matter underlying DNA are not ever-changing, but exert a guiding force on evolution.
For me, as far as the Creator, I tend to think universal common descent is so implausible and statistically insane that if it is true, it is indeed a mighty miracle of God.
I do think there is evidence for evolution, but I don't think the mechanisms presented are sufficient.
Symmetry, convergent evolution, adding of new information to genomes to go from a initial life form to all see today, and a whole host of details suggest to me that trying to pin evolution on randomness is false.
One poster argued that design was clearly there but produced by the physical properties and laws already in place.
If that is so, one has to wonder who made those physical laws and properties that hold within them the keys and blueprints of the design.