There is overwhelming evidcne that genetic change, or mutation if you will, accompanies change, but that's a small part of the story. We've only just mapped the human genome. We know little how it works. We know little what other biological structures or mechanisms may interact with the genome or what roles they may play in its change or mutation.
As for "overwhelming evidence" for natural selection, I'm unclear what you mean. Darwin theorized that random mutation would create many different versions of an organism who would compete against each other for resources until all but the best adapted to the environment have died out. Well there's just no evidence for that. If by "natural selection" you mean that life on Earth seems to have to ability to change to better adapt to its environment, well then yes, there is a great deal of evidence for that.
This is, in part, a misrepresentation of how evolution works. "All but the best adapted" do not die out. All real populations contain many variations.
Simple illustration: with the exception of identical siblings, all humans are genetically unique. this is not an unusual condition; it is the rule in populations.