If the father cannot pay support, then either the mother supports the child on her own or the state takes over, seeking reimbursement from both parents if possbile.
Yes that's right, the State takes over in the sense of Foster Care.
Parents, if there are any known, are responsible for the accrued cost of Foster Care, once they become capable of working.
The problem here is the law.
At a minimum, the law should require a man, especially young men like in this case, to acknowledge that rights to disassociate from the support order are extended for only one year. Paternity testing should be mandatory if the alleged father is a minor. If the alleged father is an adult, he should be given the option to request paternity testing at the same time that he signs his warning of a one-year limit.
I believe in some states such as California, paternity testing does not have a limit on time.
In the case here, I would think the mother should go to work and pay the state for Foster Care if she can't handle working and raising a child.
Of course she likely won't be able to pay the full amount for Foster Care on a monthly basis, so her accrued arrearages would have to be paid off over the course of her lifetime to the State.
Of course she could avoid these consequences by naming who the real father is, if she knows.
Better yet she would have a family of parents, brothers and sisters, aunts and uncles that would provide her support while she attends community college to train herself for a job that would allow her to raise her child.
But to saddle a young fifteen year old with false burden is not the answer.