Yes you can give up a child. And guess what there are thousands of parents in America who would take them in. Basically this happens all the time in the Foster Care system. Some parents are not cut out for it, neglect their kids enough for them to be taken but not so bad they face charges. They do not contest rights severance. And boom they are child free again.

So I bet your wondering if these kids ever get adopted right? There is a huge difference between a kid who went through abuse and trauma and a kid who was simply neglected. The neglected kids get adopted much faster. When a kid is placed in a adoption placement the parent gets all the information.

The worst thing you can do is abuse your kids because you do not want to be a parent. Kids who are abused are often the ones who age out of the system.

TLDR if you do not want to be a parent don't abuse your kids. Don't break any laws. Just let them be taken for simple neglect. They will go to loving homes. In my state alone there are 1000 registered adoptive parents waiting for kids. If you cannot love them, there is someone out there who will.