The "solution" here is to make conditions in those countries much worse, so that even the existing population starts to leave and the immigration gets sustained. Otherwise it will be trending down, because the replacement is no longer there and those countries will start facing labor shortages of their own in a couple of decades.
Perhaps free childcare (france), making parental healthcare free (conception to end of maternity leave for example), right to return to work laws for parents (finland iirc), tax breaks, and perhaps even an values/propaganda campaign?
I think there are economic solutions that could help, but I will admit i'm uncertain it can be accomplished in the american political environment. It would require some folks to accept there's a problem needing fixing (the kinds of conservatives who just want everything to stay the same), some folks would have to get off their high horse and realize they did a crap job of building society (boomers who think that rigging the game is a form of winning), some folks would have to accept that parenthood/mothering is a virtuous/higher calling (the kinds of liberals who think a woman who sacrifices motherhood for career is some how superior -- at least make them equal) ...
https://en.m.wikipedia.org/wiki/List_of_sovereign_states_and...