Although it's a huge simplification, I think the solution might be for the government to focus on adequate pension provision for all, combined with free healthcare for at least key health issues. Funding it is a separate (and difficult) issue !
While I'm really aware that solutions from the West are often totally wrong outside Europe (and should never be imposed !) I also think there's no harm in considering whether the lessons we learned in Europe would work in Africa.
In this case, it's notable that before around 1900, Europe had the same kind of issue with family size. In the following decade or so, most European nations bought in old age pensions (Germany was first, in 1889, the UK and Spain in 1908, etc). There were definitely cultural changes around the same time, and the quality of healthcare improved at the same time. But within a generation, family size dropped from an average of 10 children to around 2.3, as people didn't have to have enough children in the hope that some would survive long enough to look after them in their old age.