Has there truly been an African baby boom, or is it that the birth rate has remained stable-ish and the survival rate has skyrocketed?
I suspect it is a bit of this and a bit of that. It is not just child mortality, but mother mortality (during/after birth) which plummeted with better medicine, thus the same amount of women can bear more children.
But the current shape of the African population pyramid is partly determined by the baby boom in the last three generations. There were many fewer Africans around in 1963 (which is when people who are now aged 60 were born), so even if they all lived long (which they didn't), their share on the 2023 population would be much lower than in societies which barely reproduce themselves.