What percentage of women were able to have 5 kids survive into adulthood 20,000 years ago without the benefit of modern medicine. As recently as Medieval Europe as many as half of childbirths resulted in death of the mother, not to mention the frequency in which the child itself died.
Probably fifty fifty, have five kids and live to the ripe old age of 35:
Certainly a higher percentage than Medieval Europe. The middle ages had problems with sanitation and food. People coming into a new continent wouldn’t have problems with either.
When I say that, if they had 5 kids, that is net. That is including the many that would die as a fetus or prior to age 5.
However, even if you knock it down to 3 kids, it would still only take a little more than 1,000 years to do that exact same thing.
My point is that the bulk of the story is probably correct. Mathematically speaking, 70 people is a reasonable starting point for a population to start from.
The death rate at childbirth could not have been that high. Prior to hospitals, the death rate was 5-10% per childbirth. It was only in the 1800s when women were in hospitals with doctors coming in from dissecting corpses and spreading “childbirth fever” that the death rate for child birth was 30-50% - and the rate was much lower for women using midwives at home.