TNG and all the 90s shows finessed their way around the date of the Eugenics War.
The writers at the time (e.g., Moore & Braga) would rationalize in response to fan questions that the Eugenics War was going on but we just weren’t aware. Or something. But they assiduously avoided dealing with the issue onscreen despite trying to write around other inconsistencies like Klingon foreheads.
So, it was left to SNW’s Tomorrow and Tomorrow and Tomorrow to spell it all out, including moving Khan’s birth back by decades. It’s worth putting a priority on seeing that episode just for that clarity.