You still have to find both parents (or make every attempt to locate them) in order to do TPR. Once TPR is completed by the court, then you can begin adoption process. If you can't locate the birthparent, you have to show valid attempts at really trying to locate them. A judge won't TPR because you said you can't find them. You have to SHOW PROOF that you really tried - for example, by contacting motor vehicles to get address, putting notices in newspapers, sending certified mail to all known addresses..etc. If a judge isn't 100% convinced that you did everything possible short of going door to door in the state, he will not TPR. He'll tell you to hire a private investigator to find the parents. There is no way to adopt a child without the birthparents finding out about it. You have to locate that birthmother & get her consent or prove that you went through great lengths to locate her. Once she is found, they will try to find out who the birthdad is-and then probably have you post a notice in the newspaper and check the putative father's registry to make sure he has been notified of the adoption. Once you have birthparents consent OR a judge agrees that you made a 100% effort to locate the birthparents & signs TPR, THEN you can file your paperwork to adopt. You can't do it without birthparents consent.
When my wife and I adopted our son, we were told that we needed to hire multiple attorneys. One to represent the birth mother. One to represent the child. One to represent the birth father. And one to represent us. When we adopted our daughter we needed even more. One for the child. One for the birth mother. One for us. And one for each of the three possible birth fathers! We were outnumbered! Since no agency was involved, the attorney fees, the home study and the court costs were our only expenses. And when it came time to file our income taxes we claimed the adoption tax credit and were reimbursed the entire amount. Both times. We were fortunate. Adoptions can be, and in most cases are much more expensive.