Same place it always does, just print it. Of course, that still effectively penalizes those who don't want children, but the penalty is less legible to the public so there are fewer objections.
I really don't fucking know. That's not my problem. Either increase my salary by $500K for a couple years, or stop taxing me to death (state taxes, federal taxes, sales taxes, indirectly paying property taxes via rent, taxes disguised as car registrations, tariffs, so many goddamn taxes I don't have any money left to save), stop starting wars elsewhere, stop squandering money, anything.
It's not my problem, really. I'm very happy childless. Unless that money materializes, I can't afford kids.
It's just that in the US, there are 3.6 million babies born each year; even taking the low-end of a $500k one-time payment to one parent, you're already talking a $1.8 trillion / year program, slightly larger than Social Security's $1.6 trillion program.
Social Security is funded by a 12.4% income tax, with half nominally paid by the employee and half nominally paid by the employer.
You'd need a similar tax to fund such a benefit, which would amount to a 15% income tax, assuming the program isn't too successful in raising birth rates.