Unless stated elsewise, I usually assume that characters are about the same age as the actors playing them, Montalban was 45, this would have Khan being born around the year 1950. Space Seed said selective breeding, and Khan doesn't seem like a first effort, so the breeding program started maybe in the nineteenth century.Kahn was atleast 30 when he went into hibernation in 1996. That means that the science that concieved him was in place in 1966.
Voyager traveled back to 1996 and yet we saw no indication of any sort of global struggle against genetic supermen
The 21st century is supposed to be a reach bitch on humanity, yet some kind of way we still manage to have an incredibly robust space program.
Previous world wars didn't actually involve fighting across the entire world. Perhaps one of the reasons Earth recovered as fast as it did following WW3 (sixty years) is that those countries best able to assist in the rebuilding largely sat the war out."Post Atomic Horror"
Similarly, Los Angeles looks the way it does in Past Tense is because America wasn't heavily involved in the Eugenic Wars. This might also explain the ability to have a robust space program.
And you could have a post war horror in one or two countries and have it be historically infamous, but the rest of the world never had anything remotely similar.

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