Down syndrome in subsaharan populations
See UN > stats Down Syndrome per country.

What the data says

I have not made a proper statistical test (as I am too lazy to reformat the data in anything convenient to perform a statistical test) but the prevalence seems to be consistently around 0.12499% all around the world with very very little variance. I doubt there is any significant difference in the frequency of birth that have down syndrome.

As @Markonionini rightly noticed, these estimates of prevalance are slightly far fetch extrapolation and the UN specifically advice to consider them with caution. It is probably the best data we have though.

The hypothesis seems improbable to me

Do you have any good rational behind your hypothesis? Down Syndrom is typically caused by de novo mutations and not due to standing genetic variation (Veltman and Brunner 2012) so your hypothesis seems rather implausible to me.