As an adoptive mother of two, I can safely say that Laura is correct. After initial filing, it takes six months to get the hearing. At any time during those six months, the biological parents can reclaim their child.
We've gone through private adoptions with both our boys, so we never had to jump through a bunch of hoops to be matched or approved. Those take a year or more, requiring criminal background checks, financial checks, psychological evalutions, health exams, and on and on. But with a private adoption, the biological mother signed away her rights, in front of a lawyer that we had to pay for, then we had to inform the biological father. In our case, we ran an add in the paper for three weeks. Once he failed to respond, the official paperwork was done to take away his rights. Then the waiting period began. At the end of the six months, we were issued a court date, assembled for the hearing and pronounced proud new parents! (Although we'd already had both kids since birth.)
As a side note, in an adoption, not only do you have to have a lawyer, but the baby does also, usually called a guardian ad litem. Then you have to have another for either parent or both that sign voluntarily. That could be a grand total of 4! But still considerably less expensive than a state adoption.