While I personally think your idea is likely, you really only need people to live to be about 50 or 60 to accomplish this, I think. If every generation has kids

While I personally think your idea is likely, you really only need people to live to be about 50 or 60 to accomplish this, I think. If every generation has kids from around 15-20 years old, which seems very likely in our distant past, then you only need to be about 60 to have three generations of descendants (children, grand-children, great-grand-children), in which case by this argument perhaps you've done enough already and are free to die by whatever means you prefer after that point. Maybe our advantage was that we, unlike other primates, had a lot of individuals even only making it to 40 years old in the distant past before they got eaten by tigers or succumbed to all manner of mosquito-borne diseases et cetera.