Hi OP. For what it is worth I think you have had some very harsh comments on here from people who have nothing more than a snap shot of the situation. I have assumed that you after a legal perspective rather than anything else.
Basically as your partner is on the birth certificate he has parental responsibility for the child. This is why he has been informed by social services of the situation. The first thing he has to do is get legal advice. If care proceedings have been issues or a pre application meeting has been called ( he would be given official notice of this) then he is entitled to legal aid irrespective of his income or assets. Child care solicitors are very issued to proceedings be issued quickly and can usually offer appointments at very short notice. If you can try and find someone who is on ' the children's panel' . You can find this out by doing a search with the law society.
What you need to think about as a family ( and be ruthlessly honest) is what you would like. If DNA is in dispute the court with order a test ( paid for by legal aid). If he is not the father his involvement will end.
If he is the father and he doesn't want anything to do with the child loving forward He is not legally obliged to. He can simply say that he will support whatever is in the best interests of the child and walk away from proceedings without any judgement or criticism.
If he decides he does want to be involved he will need to be fully committed. Whatever the future holds he owes to the child that if he starts to spend time with her then he doesn't plan to stop doing so at any time in the future.
It sounds as though his position if he were to get involved would be to support the child returning to mum if it was safe and appropriate to do so but offer himself as an alternative carer if it was not possible.
The child will have her own guardian appointed to look independently into what is in her best interests and this guardian will also have a lawyer.
As a family you have some big decisions ahead but the first port of call should be legal advice but please so this ASAP and as it will be free you don't have to worry about that side if it at least.
Lots of luck to you all.