Ooku/WMG

The Red-face Pox made it across to the mainland and has Gendercided the planet by the time of Chapter 1
The odds of a carrier fleeing the plague making it across the Sea of Japan before the order to seal the borders are pretty good, and once it got going in China/Korea it is a matter of time before all of Eurasia is hosed.
 * The habitual stage managing of the VOC's contact with Japan succeeded convincing the Dutch that Japan still has it's men, so they stock Deshima with crossdressers and whatever fellow past his breeding prime they can spare for a front man when close-range meetings are unavoidable.