The GI bill is American; the baby boom is not. Other countries saw the same phenomoenon.

https://en.wikipedia.org/wiki/Mid-20th_century_baby_boom

If people think at all rather than just doing what everyone else does. People invest in their future. Peasants don't own land, can't own land, have zero access to financial wealth or education, so they try to breed because adult children are the only type of family wealth they can produce.

Baby boom is those people with that mindset with some sudden prosperity.

Doesn't last as soon as they see the successful people invest in land, financial assets, material goods, and children's education. Base culture matters, you saw Confucius based cultures turn on a dime once they had two to rub together.

I think it was having a government having an active hand in guiding society: housing, education, childcare, stable government jobs, high enough taxes at the top end to finance all of that.

Every major economy was either running at max capacity due to the war effort or was in desperate need of repair and reconstruction. The US starts handing out loans like candy to a) help rapidly rebuild the economies of our allies and trade partners and b) fend off communism. So here we have...

1 - Millions of men with newly gained skill eagerly reentering the workforce 2 - A surge of highly skilled immigrants/refugees 3 - Trade partners rebuilding rapidly using US loans to by US goods (as the US had emerged as the world largest manufacturer). 4 - All of this happening with the benefit of countless technological breakthroughs brought about by the war effort.

It's these anomalies that led to the very temporarily rise of some men in some parts of the West being able to support a family of 6 with a single job and minimal skill or education.