I'd be surprised if there is no company running such a business, probably a more traditional one, not an SaaS one. At least in China I know there are companies

I'd be surprised if there is no company running such a business, probably a more traditional one, not an SaaS one. At least in China I know there are companies that run business taking care of registration (and other chores) of new companies. It may take months if you don't use their service, but maybe merely a couple of weeks if you do.