So all but one of the current main originating countries with higher birthrates than the US. As noted, several with their own birthrates recently dropping modestly below replacement level. But you are located on the other side of the pond? And there the main immigration groups are those welcomed from Ukrainians and Belarus, and the not welcomed Syrian refugees and those from Africa.
I am interested though in thinking ahead, and I am clearly repeating myself by now: there will be climate refugees. Declining birthrates won’t be the existential threat to a country when your major coastal cities are flooding and/or you cannot produce or purchase enough food.
I get your fear of your national character being swamped by fundamentalist believers of a faith you do not share.
And you get that there are no practical interventions to bring declining birthrates back to let alone over replacement levels.
Hopefully you appreciate that the rightist fantasy of a return to women knowing their place was pregnant if not barefoot, is not going to happen even with regressive policies. Encouraging those as social values would likely ironically lower birthrates catastrophically.
So there really are not too many choices. We work around the edges with interventions that have modest impact, like subsidized childcare, and maybe some corporate support for flexible schedules including work from home explicitly as support for parenting by both mothers and fathers.
And the shortfall has to made up by welcoming immigrants in a controlled manner and appreciating the positives of a pluralistic society.
And also hoping that technology helps out with increasing productivity too.
There simply is no other choice than hurtling to a graying society abyss.