Israel is also booming economically as it is the 24th in terms of GDP per capita now and rising: https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nomi... Israel has the 2nd largest per capita VC investment in the world: https://news.crunchbase.com/news/countries-most-startup-inve...
What are they doing that others are not?
The US has a similar fertility-focused religious movement, but it's much more fringe and relatively smaller. Religious beliefs can drive super-high birth rates in pretty much any society, but aside from Israel, higher education has been associated with lower rates of religious belief. Declining religious participation and intensity of belief may well be contributing to the fall in global birth-rates.
1) immigration - of course Israel grants the right of every Jewish person to live in Israel, in fact paid an incentive to relocate. Presumably there a constant inflow from the Jewish diaspora and their descendants which might supplement the population
2) orthodox families, I'm guessing, have outsized families. Where women do not participate in the market economy, they end up having lots of kids instead
Again, no idea on the percentage contributions of either of these cases, but it might go some way toward explaining Israel's countervailing trend!
It's not just women. Somewhere around half of Haredi men do not work.
Or, stated less pejoratively, somewhere around half of Haredi men devote their lives to scholarship.
https://www.timesofisrael.com/haredi-population-growing-twic...