No, natural selection isn't random variation. You're confusing mutation (which sometimes occurs because of random variation) with natural selection, which is something altogether different.
would not favor anyone it selects, and how would it know to select milk drinkers.
On the contrary, if milk drinkers were better nourished than their non-milk drinking neighbors, then they would be more likely to survive to reproductive maturity and natural selection would certainly favor them.
Natural selection is a random act that brings everything back to the average.
You got it backwards. Better genes tend to survive. If someone has mutated genes that increase their chances of survival over the average, natural selection will favor them.
how would it know to select milk drinkers
It doesn't. People who are better nourished are more likely to survive. People who can drink milk are more likely to be well nourished. That's natural selection.
. But the 3000 year thing is close to Biblical flood time of around 4500 years when God told man to eat meat.
Did you read the article? There were at least two independent mutations. One that allowed East Africans to drink milk, about 3000 years ago. An earlier mutation allowed Northern Europeans to drink milk, 6000 years ago. You are really a one-track record --- you'll read your creation myth into anything. If you were a contestant on Jeopardy, I suspect every answer would be "What is the Noahic flood."