>They could win via superior manufacturing capacity and the sheer number of people they can draft into service at a moment's notice.

Even with their manufacturing capacity they don't have remotely enough boats to get a nontrivial fraction of those people to the US mainland, and the majority of those people can't swim, so they wouldn't help in taking the US mainland, a requirement to "win" a serious war. Their entire armed forces is also almost completely lacking in combat experience, and in their last skirmish (against some unarmed Indian soldiers in the mountains) 30+ soldiers Chinese tragically drowned, due to the aforementioned lack of swimming ability.