Adopting a second/third child that has been put to adoption due to the law

Can I adopt a chinese baby that was born as a second or third child and has no legal existence? What I am referring is to the children who have no access to a birth certificate, education, or healthcare and are sent to orphanages. I am an american citizen and I would be very interested in adopting these children that have no recognition in China. Can I adopt them and make them american citizens through any method?
Thank you!