As far as I know there is no way to increase birth rates. No formula, no payout, no policy that will guarantee that a country will have more births, except maybe a bump.
[1] Israel has been in a constant baby boom since independence, with the highest fertility rate in the OECD at 3.1 children per woman. - https://en.wikipedia.org/wiki/Baby_boom#Israel
You think everyone should become a bunch of religious nuts? That's not something that's exactly easy to instill in a population; it takes generations. It also usually results in a lot of bad things: oppression of women and minorities, warmongering, etc.
Religion and fertility may be correlated, but it's demonstrably not an unbreakable rule, and outliers abound, so we shouldn't just give up. Sources:
https://en.wikipedia.org/wiki/List_of_countries_by_irreligio...
https://en.wikipedia.org/wiki/List_of_sovereign_states_and_d...
> known reliable way solution that generalizes
Why all these qualifiers? It doesn't have to be reliable or general - individual countries can each have their own approach, that only works after lots of tweaking, and even just intermittently, as long as it time-averages to replacement level. And it won't become known unless we look for it - more than the occasional sporadic attempt by a government that gets decried as racist and sexist for their efforts [1].
> exactly like Israel
Why "exactly"? If someone pointed to Japan when searching for solutions to reduce heart disease or medical costs in the US, would you also say "become exactly like Japan" isn't an option? Many countries similar to Israel have low fertility, while many very dissimilar ones have high fertility. Clearly, being exactly like Israel isn't necessary.
[1] 'Baby machines': eastern Europe's answer to depopulation - https://www.theguardian.com/world/2020/mar/04/baby-bonuses-f...
That sounds like an unending series of demographic shocks and may well be worse than the original problem.