In the US, everyone who's in foster care starts with a "return to parent" case plan, and the parent has 15 months to get their act together and improve whatever circumstances led to the child being in foster care. If you look at an individual case plan, a regular foster placement would mean that you would get the child immediately when they enter the system, which here means that you frequently get newborns. A foster-adopt placement means that you don't get the child until the case plan has changed to adoption, and at least one of the child's parents has had their parental rights terminated. Given that everyone starts with a "return to parent" case plan, a foster-adopt family typically wouldn't get a placement until the child had been in care for at least 15 months. This most often means no newborns or young babies, and placement of kids who have lived with their first family, a foster family, and then are moved to your family. We wanted a child placed with us immediately when they came into the system, which is why we chose to do foster care, rather than foster-adopt. We ran the risk that the children would be returned to their parents, but with the two children we wanted to adopt, we just got lucky. Our son was 23 months, but we were his first licensed foster placement. Our daughter was one day old when she came home. With our daughter, we knew we had a good chance of eventually being able to adopt her, because her birthmother had already had her rights terminated on her prior 3 children, and there was no birth father named. It was risky, and we had to wait 18 months to finalize, but it did finally work.
To contrast, though, as foster parents, we have also had over a dozen babies stay with us and go home or go to a relative placement. None were children we wanted to adopt, but if you don't want to take the risk of falling in love and having a child leave, regular foster care isn't a good option for you.
If you want a totally hassle-free adoption of a very young baby, private adoption is the way to go.