I am going to assume that although she signed the paper giving you temporary guardianship that no case was ever filed in the Superior Court so you have never been legally declared as the guardian of this child. With any non-relative adoption a Home Study will be required and this should be started IMMEDIATELY. The next step is to contact the mother about whether or not she will consent to the adoption. If she is willing to agree to the adoption, you will need to take appropriate steps to terminate the parental rights of the father. If you do not know where he lives, notice by publication may be appropriate. I am assuming that the mother was not married at the time of conception or birth of this child. All the paperwork is filed with the Court and a hearing will be conducted. Please keep in mind that Georgia has very specific forms for an adoption. You should definitely contact an attorney as soon as possible. Best of luck to you.
This information is provided as a public service to provide a general answer and should not be relied upon as legal advice.