He got out of jail and now is in sober living. But there was some time inbetween and in that time he did NOT ask to visit his daughter (either by message or directly). He didn't lift a finger to see his newborn baby? I wouldn't bring the baby to him. A loving father of a new baby will move mountains to get a glimpse. I don't use addiction or recovery as an excuse either unless he is inpatient in which case a counselor would have been the intermediary.
You have very good instincts on this one. He has not shown an interest in being a father. Not only that he has shown no interest in even bonding with the new baby. Even if he didn't have the capacity to parent, he should take an active interest in knowing her. I have never heard of a newborn baby brought to the new dad unless he is locked up or in the hospital hooked up to life support. Those are the only two excuses I'd accept
Not sure where he staying but sounds like an intermediary would help you.. a professional one like a social worker, counselor, LAWYER