Mutation. Radiation or reactive chemicals come into contact with the DNA (via "the environment") and cause it to have a different chemical structure — i.e. a different gene. New genes are created in this way, and completely randomly. The genes can either have a good, bad, or nonexistent effect, and the bad ones are weeded out by the environment killing of organisms with them.
Only if the selection pressures on them never changed, which, over a million years, is fantastically unlikely.
This implies that genetic diversity is somehow inversely proportional to intelligence, which is nonsense. They're independent, roughly. To preserve genetic diversity you'd only need to leave enough alive — somewhere above ten thousand. That would leave sufficient diversity to account for any future environmental changes. To prevent inbreeding you'd only need a population size above five hundred.
No, the environment did it for us with as yet unclear mechanisms. Most of Holla Forums theorizes it to be drastic environments requiring future-planning, but that's only one theory.
On what basis is it impossible to mutate a beneficial allele or gene?
No, obviously the creation of nothing but beneficial genes by a random process is ridiculously improbable, but that's not the mechanism. Mutation creates random genes and alleles for good or bad, and if they're bad the people with them die off. Rinse and repeat many times with only those with good genes surviving and you end up with a population whose genes were "materially bettered," to use your phrasing.
You could probably go into realistic specifics, such as your morals leading to better outcomes for populations via civilization, but beyond that there is no objective way to convince them, I'm afraid. At that point they have rejected the concept of truth and logic, and you can no longer argue with them. There's just no point, and you need to accept the only solution to your disagreements is a life-or-death struggle.
If you're trying to pitch that to leftists it wouldn't work because they're not actually arguing about "justice," "fairness," "oppression," "privilege," or any of that garbage. Look past their words to see what they're really saying: "Give me more free shit." That's all they want and they'll say and do whatever they have to to get it.
There is no (non-biological) "white privilege." They don't believe it, and neither does anyone with a brain. They don't actually care about it or whether it exists, they only care about how much money complaining about it will get them. Like a spoiled child crying to get goodies from its parents, these people are not wounded or hurting. They are only seeking material wealth, and if complaining about "white privilege" gets them it, that's what they'll do.
You won't get anywhere with your argument, is what I'm saying. It doesn't address what they really care about, and so it'll be rationalized or ignored. You will always be racist because they will always want more stuff from you.
Don't be like braindead good goys who are senselessly committed to only ever arguing at face value. Ignore what their words mean and see what they're really saying. Just like you shouldn't believe that North Korea is a "Democratic Republic" so you shouldn't believe that (nonwhite) leftists care about "white privilege."
If you're pitching it to anyone right-wing (that doesn't mean cuckservatives) they won't care so long as the nonwhites leave. There's no point in trying to sell them on what might be in the black interest, because that's not their concern.
TL;DR: that argument won't really be useful.