Generally, unwed birth fathers seldom come forward to contest adoption, but occasionally they do. The rights of unwed fathers vary. In some states they have rights equal to the birth mother's; in others they have almost none. It is important the father's rights be understood, properly dealt with, and never ignored. Adoption is easier if the birth father will sign a simple waiver and furnish medical background information about his family.
For the most part, however, unless a birth mother is married to him, or he has affirmatively asserted a paternal interest in the child, adoption may be accomplished even if a birth father is hesitant to sign papers. There is generally no problem if the father's identity or whereabouts are (truly) unknown.
Each case is different and I can't give specific advice without first discussing a situation with the parties involved. You can be certain that the father’s rights will not be ignored!