No one has found or discovered such policies that work across-the-board.
But blaming the poor young people priced out of their own country for not breeding, and just bringing third world immigrants with no living standards, is much easier than improving the living standards of your own population.
As long as you treat housing like a speculative investment that is squeezing the young to get a much larger return for the older owners, instead of treating it like shelter and a basic necessity for any family, why are you surprised young people don't breed anymore? The precarious job market isn't doing them any favors either.
Mass migration that puts more pressure on affordable housing and on the low-end jobs market is not the solution here. That breeds long term instability, segregation, distrust, and leads to political extremism. The solution is fixing housing, which nobody actually wants to do, because "housing prices must go UP", and the ruling asset owning class is making a killing from it.
Guarantee all parents affordable child care close to their work or home and many people settling for one kid will have two.
Sweden has that (and generous parental leave policies) and still has both low and declining birth rates.
Maybe a lower population -> lower housing prices -> easier to start a family will cause some sort of equilibrium.
That's not how real estate pricing works in the real world capitalism. Germany's population has been on decline for ~30 years due to demographics, yet housing has been getting more and more expensive, far outpacing wage growth in the last few decades, especially after the QE bull run from ~2013, so much so that owning your home is impossible for the average German.
Why is that you wonder? That's not how free market economy should work right? If now there is less demand for a good due to population shrinkage, then prices should come down right?
Well, that's because housing is not a good, it's a speculative investment asset, so as soon as people die and are not replaced, their free houses don't magically end up in the hands of those who would need them the most to buy at a discount, but end up on the "free market" being bough by existing rich home owners, investors, speculators and publicly listed real-estate conglomerates, using their existing assets and capital as leverage to buy even more houses for their investment portfolio. And governments and banks have ensure the policies to make sure this asset keeps going up, up, up.
When housing is an investment vehicle, then it can never be affordable, regardless of the population decline.
Like a commenter above said, which explains why home prices are not coming down despite population shrinkage: "people are not competing for houses, piles of money are. The bigger piles are winning."
The thing is – within that time frame it hasn't, actually. There have been some years with slight decreases, but those have been balanced by other years with increases, and compared to 1990 population is actually definitively slightly up (83.2 millions last year vs. 79.8 millions). Combined with a decreasing average household size (2.27 in 1991 vs 1.99 in 2019) and internal migration those things by themselves will probably generate enough pressure on the housing markets in and around the prospering parts of the country, even without any added financial shenanigans on top.
Fix those first so we can have a stable income and affordable housing from a young age, and then we'll take off the condoms.