I would think increasing immigration would actually achieve that better, at least when we're talking about immigration from places with worse access to education to places with better education.
Better-educated people (especially women) seem to tend to have fewer babies. (Note that I'm not making a value judgment here.)
And beyond that, to avoid demographic shocks, you probably do want to bring in new people from elsewhere to help care for the aging population that's now much larger than the young population, after the birth rate has been below replacement for long enough.
Granted this is a zero-sum game: countries that lose their young people will end up being worse off, while those that aggressively pursue new sources for immigration will benefit.
We always talk about taking care of the aging population without talking about the other side of the coin, society also have to take care of the kids, the cost is somewhat ignored as those kids will turn into adults at some point, but it is still part of the chain.