I'm certainly not a lawyer, and am only basing my answer off what I've been told and learned myself.
If paternity has been established then the child's father must be informed that the mother wishes to place the child for adoption. And if no courts have been involved then the mother doesn't have *sole custody* even if the child has always lived with her and never the father. I believe custody can only be officially established through the courts. I THINK there is a loophole, where if a parent has had NO contact with the child, or other parent, for over a year that the parent is considered to have no parental rights... but I could be very wrong about that. Plus, from what you've said that doesn't apply to this situation anyway.