Adoptions can sometimes be arranged without an agency. Initial contacts can be made directly between a pregnant woman and adoptive parents or by the pregnant woman and an attorney, depending on state law. Independent adoption is legal in all but a few states, but there are significant variations regarding specific aspects of adoption laws of which you should be aware.
If you pursue this approach, retain an experienced adoption attorney to explain the adoption laws in your state. Talk to other adoptive parents. Become familiar with the Interstate Compact on the Placement of Children (ICPC), because in interstate adoptions you will be required to comply with the adoption laws of both states. You certainly do not want your adoption to be challenged because of failing to comply with the relevant adoption laws.