Although laws vary accross the country in adoptions, typically once the birth parent signs and/or a judge makes a “final” ruling in the adoption the birth parents can’t come back and get the child.
When this does happen, typically there has been a finding of fraud. However, this is very, very rare.
I hope it is rare now, I know in the 80s there were several cases of birth moms changing their minds and being allowed to take back the baby for something like a year.
How long does it take for the judge’s final order? I know I could not take a baby for months and give it back. I would lose my mind.