Not the only one, another is to give economic incentives for having children. Sweden has a general payout to families per child, it was created for the same reasons.

Not the smartest thing to do when you give people a monetary incentive to have kids... especially people who should not have kids.

Bad kids/people cost more than no kids/people.

Kids cost a lot of money, the government can give a lot without them being a profitable proposition for the parents. Aid to families would only be a help to those who want kids but can't take the economic risk.

Yes, but that only works in the VERY long term. Suppose you doubled the birth rate now - the effect on the working force would only be felt after at least 20 years.