And, now, if the info is correct, we have another date point for the Eugenics War, these wars occurred in the 1950s. (300 years before 2259.)
Not really. "300 years" is probably just a generalized figure tossed out at random.
It's not like a specific year is mentioned, is it? They only do that in 'Space Seed' and TWOK. If they give a year, then that's definitive. If it's just a round number of years, it's not. That's how I look at it, anyway.