"She did not drop him directly off at an orphanage, so she can’t tell anyone where the boy is if questioned under magic. Many muggle-borns have managed to perform accidental magic in all sorts of environments, and places like orphanages are generally only monitored by the Ministry at a distance; if the child reaches Hogwarts age, they are sent a representative and allowed full scholarship to the school, but before then are left completely alone. Their magic is generally allowed to mature fully, although of course growing up without a family is... a different matter."