No country will ever convince native populations to have more children solely because of immigration [1] (Utah and Israel do it with religious fundamentalism, which has...fallen out of favor, broadly speaking); immigration improves the economy, which creates economic potential for native born to potentially consider having children. You're never going to convince most rational people to have kids in a poor economic macro (Russia, South Korea, Italy, Greece to varying degress), so you must stoke the economy to ensure it is sufficiently healthy to encourage those still considering having kids to have them. Immigration most recently was creating a robust US economy, for example [2]. Of course, a robust economy is no guarantee you're going to convince native born citizens to take on the burden of childrearing. Raising children is incredibly high cost to parents and the rewards are mixed at best.

Your comment here [3] leads me to believe that rational arguments are going to fall on deaf ears though, from the anti immigrant pro native born vibes. Correct me if I'm mistaken on that though if I'm misreading the comment.

[1] https://news.ycombinator.com/item?id=44229099

[2] https://www.axios.com/2024/03/13/immigration-economy-jobs-gr...

[3] https://news.ycombinator.com/item?id=44230345