Hope someone can help.

What I found out about this:
- If a man hasn't acknowledged the child and isn't involved in raising it, he has no rights. I don't see anything in your story about a cohabitation agreement or marriage, because that would change the situation.
As for criminal liability, as long as the father doesn't have a visitation arrangement, I believe there's nothing to worry about.
But well, I'm not a lawyer or anything like that.
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However, if the man has no relationship with the mother, or only lives with her, he does not automatically acquire the status of legal father. In those cases, the man must acknowledge the child. This can be done by registering the birth at the municipal civil registry office before or after the birth. If the man doesn't do this, or if the woman doesn't give consent, no legal family relationship between father and child will be established. This doesn't mean that a (biological) father has no rights (or obligations) towards the child.
If a father hasn't yet acknowledged the child but is involved in caring for and raising it, he can claim certain rights, such as the right to contact with his child.