I was thinking about this, and have a ton of different ideas.
1)It starts right off in the cave, with Ryo and Shenhua possibly discussing what just happens. There could be a possible event to start the game off in the cave, because it seems like there is more to it.
2) Something more similar to the beginning of Shenmue II. It have an opening scene of Guilin, and eventually show Ryo and Shenhua back at her house, walking to Bailu Village, or the same thing was my first thought, just have an opening scene first.
3)I also thought that the setting of shenmue III could change a lot. We might follow Ren catching up with Ryo a little bit, or Gui Zhang finally coming. Or it could go back to Xuiying, and show some stuff with her. Possibly even back at Yokosuka, and have a scene with Ine san or Fuku san, who knows?
4)A lot of people think because of very different setting in shenhua's first flashback, the baby could be one of her ancestors. They could have occasional flashbacks telling her story, and starting the game off with a flashback would be a good starter.