Something bring the birth rate up. The world is losing some genetic diversity as some groups like the Japanese are not passing most of their genetics on.

I have no idea how to get people to have kids though. Some things like child care, time off for kids, and different taxes can be tried, but are they enough?

Perhaps the only correct solution is a combination of methods: selective immigration + programs that make it easier to have children + maybe some state propaganda (state propaganda can be good, though not always is) + other approaches.

When you think about it, it really seems like a gigantic task

It's not really a gigantic task to offer perks for families(i.e better loan rates, childcare services etc)and you don't need any immigration. Of course you need some positive discrimination ajd perhaps propaganda as well. You get propaganda anyway (i.e a while ago we had a lot of war propaganda<i.e on terror>, nowdays we get a lot of LGBTQ propaganda) so it's not "bad" per see as long as it's acknowledged and serves the common good. I would take that over the "we need cheap labour/immigrants with unlimited visa to sustain our economy" propagabda.

The question is will those things work. Will people ignore your perks and propaganda and continue not having kids? I do not know. Finding what actually works might be a gigantic task.

I don't think it would suit retirees, of whom there are many)

Well they are gonna have to do it for the sake of glorious nation of Nippon if they don't want immigrants

USA ships them to Mexico in exchange for cheap labor