Maybe we as a society should decide that having children is fine when you don't have a stable career yet and finance it as such. The contradiction that our most fertile years are also the most unstable is something society could and should balance.
Definitely, but having children when you aren't stable yourself and society isn't going to help out much could wind up in disaster. "Let's play life on hard/hell mode" doesn't really sound appealing to me.
There are things we could do as a society to make this easier: socialized child care (like we do with school) for one thing. Better welfare, making it easier to go to college when you have kids, etc...
But we aren't really doing those, most definitely not doing those in the states, and even in other western countries with better social safety nets. If you want society to have more kids, maybe we have to socialize child rearing more than we do today?
EDIT: typo