As the top answer in the linked question indicates, this sort of mutation is a very serious problem for humanity which fortunately can be quite easily mitigated with modern national- and international-level identification and amelioration programs. So it is essential that your story begins prior to the discovery of modern genetics at the beginning of the 20th century. Scientists of the Mendel-era might have been able to identify the mechanism behind the illness, but would have been powerless to identify which of a given collection of human males had, or did not have, the mutation.
I'd say any time before 1900 is fair game for the mutation surviving and posing an significant threat to humanity. But you want the mutation to threaten all humanity, and that requires a very broad dispersal across ethnicities and cultures as well as geographically.
The best vector for such a dispersal is a large body of men with a high proportion of 'infected', travelling into new populations and procreating with a large number of native women, disregarding normal monogamous family groupings within that population, and leaving the male offspring in the destination population. That unfortunately describes pretty accurately the conduct of all armed forces prior to the Second World War, and a depressing number since. Armies being the main vector makes a lot of sense in all sorts of ways: infected monogamous families will have a large population of sons, and 'second-plus sons' are more likely to join the army. Meanwhile soldiers prior to the 20th century would spend years at a time away from their families, making the increasing gender disparity harder to identify, while the wives of soldiers away for such a long time might have daughters from, ahem, 'other sources', further complicating discovery.
My suggestion is that the mutation breaks out in early- to mid-18th-century Western Europe at the height of the Age of Empire. At this time the European nations were rapidly expanding their military and economic tentacles into the New World, to either civilise and enlighten, or rape pillage and plunder (depending on your perspective) these new lands. While the mutation hollows out the demographics of the Old World populations it would be spread to all corners of the globe by sailors and soldiers.
The consequences of this could be quite wide-ranging, and would certainly make a big impact on history. The empires of the old world would probably collapse from within as their demographics skewed beyond recovery, leaving the fledgeling colonies independent much earlier than in our history.