A much bigger reason for low births is insane housing costs. The price-to-income ratio in cities like Shanghai or Beijing make even London look cheap by comparison. Who is going to have kids if you can't afford big apartments and/or houses relatively easily?
Another issue is lack of religiosity. Religion drives fertility. For an atheist nation there are hard limits. Maybe China can get to Japan's 1.4 TFR from today's 1.1. The key issue should be to avoid rock-bottom TFR like South Korea's 0.8 TFR.
Religion isn’t useful as people would normally expected, just look at Saudi( most devoted Muslim country?) or SK( currently one of the most Christian countries in the world) , once industrialized or partially industrialized or just being exposed to industrialized world, birth rate just drop like a waterfall, immigration could help, but not for long.
I get a feeling that whatever you do, once it dropped, it’s beyond save , about housing costs , which is far worse in China than in the US, but I don’t see Chinese immigrants living there having a significantly higher birth rate anyway .