China doesn't have any problem for having big families even during the height of cultural revolution and when atheist is on top and that all types of religion are under attacked. In addition, Chinese worship ancestors from ancient time and never very religious. Somehow it has become the world most populated country. So your assessment of religion drives fertility is false.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 and atheist have nothing to do with fertility. The only reason why some religion drives up fertility is due to brainwashing and propaganda. Even Muslim countries, India, and many Latin American nations are having lower fertility over the years. Urbanization and women empowerment and education, and low child mortality are what drives low fertility.
President Xi understands the importance of work life balance. That's why he has tried to crack down on property prices, tutoring and tycoons. Common prosperity is strike to find a road for high and middle and lower income Chinese so they wouldn't be enslaved by the corporate like the Japan, Hong Kong, and South Korean tycoons, conglomerates and zaibatsu did to their people.