Adoption is easier if the birth father will sign a simple waiver and furnish medical background information about his family. Generally, unwed birth fathers seldom come forward to prevent adoption, but occasionally they do.
The rights of unwed fathers vary from state to state. In some 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.
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.
Of course, each case is different and I can't give specific advice without first discussing a situation with the parties involved.