I think we're overlooking the beneficial effects of policies that aren't explicitly pro-natal, like the reforms to private tutoring and deflating the real estate bubble. If carried through and properly enforced, these policies will remove the two biggest economic disincentives to having children. I hope to see more efforts to regulate working hours in China (none of this 996 bullshit) and enforcing a healthy work-life balance. My feeling so far is that the "Common Prosperity" program has a lot of such goals in it, even if it doesn't explicitly state that raising birthrates is its objective.
There are other quasi-economic steps the government could take, which I consider "redistribution of opportunity" as opposed to outright redistribution of wealth (which should certainly be done as well). For instance, I think better educational opportunities like placement in better universities, as well as better job opportunities should be given to applicants with at least one sibling.
But the stickiness of this issue is cultural. Even if having children is economically incentivized, the culture will continue to have a retarding effect. This is why I focus on the point that having children is an emotional decision at least as much as it is an economic one. This is where the Chinese government will have to be more subtle than in the economic sphere. It must mould and guide the culture toward shedding anti-natal and anti-nuclear family elements and raising pro-family ones. What's needed here is a sustained and massive advertising campaign to encourage having children like the old advertising campaigns cigarette companies waged to get people to smoke.
We can view this through an economic lens by considering the "prestige economy." A lot of people's behaviours aren't just to acquire material wealth, but the more nebulous and vague prestige (or "clout", as kids these days put it). Having kids should be seen as accruing prestige, while being without marks one as a loser and failure.