The rather inaction of the central government of China in addressing this urgent issue is truly beyond me. Merely lifting the limit from One to Two to Three-Child Policy WILL NOT WORK.
There needs to be significant, and I mean SIGNIFICANT, economic and societal benefits and incentives offered by the government to the people in order to encourage them to have as many children as possible.
They didn't have any expectation that lifting the limit to three child would fix the problem, they were aware of the problem long since they found out that increasing the limit to two child didn't stabilize the birth rate. The increase in the limit is to signal a shift from a policy of passive and unurgent encouragement of birth, to a more proactive and urgent encouragement of birth.
Many provinces and cities are testing out benefits and incentives, each with different measures according to their capacity for funding and for testing. Having significant benefits and incentives alone, doesn't guarantee the birth rate will be stable in the long-term, and its extremely costly as well, we can see the result of these policies from other aging countries in Europe and Asia. What needs to be done is to tackle other factors that negatively affect birth rate that wasn't done in other countries, like controlling housing prices, reducing childcare and education expenses, making the environment that promotes socialization and fertility, and reintroducing the family values that much of the current generation have lost due to modern pressures and urbanization.
The result of all these incentives the provinces and cities have enacted recently is still to be seen. It would take at least a year to determine if the benefit outweighs the cost, or if there needs to be more supporting measures to achieve the desired result. They shouldn't just enact all birth rate supporting policies they have in mind, what's equally worse to having a low birth rate, is having to spend 10%-20% GDP just to put birth rate at replacement levels, and may lead to unforeseen negative economical and social effects.
China is neither a low-income country nor a low-literacy country anymore. That means China should understand that with the living standards of the people being massively upgraded and improved over the past decades, people would no longer produce children like rabbits anymore. Therefore, this should remove the worry that the population would explode again like in the past.
Last but not least, the people should be reminded that they are the fundemental building blocks of their own homeland. If they want to do their patriotic duty as a patriotic citizen, they should give a hand in preserving their home country and helping their own homeland to have a more secure and brighter future.
One exception to the correlation of developed country status and low birth rate is Israel, the reasons for that is I think have to do with their religious familial practices and beliefs, but they are also coupled with support and benefits to incentivize child growth. China doesn't have to adopt a religion to achieve similar result, they could instill those belief as an ideology like you said, making it a patriotic duty to create a family. But instilling those values alone is not enough, there needs to be promotion of behavior based on those values, like for example, extended family should become the norm, where the elderly would look after their children's children, communities are formed made to support one another's childcare and maternity materially through gifts and babysitting, and celebrations/holidays made to celebrate maternity and children to elevate their status and practice behaviors to help ease the burden of childcare temporarily.
All of these solutions would need planning and time to execute to its fullest extent, but personally I think the closest thing to a silver bullet to this problem is development and maturation of Artificial womb technology, and fortunately there are signs of this technology being explored, like I think few months ago there's news of Chinese scientist creating an AI to monitor fetus development in the womb and can possibly used on artificial womb technology as well, and although this is an insignificant point, Elon Musk is also looking into artificial womb technology, and express interest in investing in such. For now China can prepare to dampen the negative effects of an aged population, through heavy investment into AI and automation, and modernization of industries and supply chain, while also see if they can slow down or even possibly reverse the trend of aging demographic problem using the solutions we discussed in this thread.