If I can choose the US specifically, then sometime in the 1950s. I think Baby Boomers in the US will go down as the single luckiest generation on earth in terms of socioeconomic opportunity.

Yeah, I don't disagree, but if we're talking about how our species (which I took "civilization" to mean) as a whole has fared, I think you shouldn't get to pick the where, just the when. If we care about all humans everywhere, and whether fewer of them are starving or dying of preventable diseases or whatever, then I think you have to consider being born as just a random human, not just a random American.