Can I do a private adoption in New York without going to court?

I’m pregnant and I do not plan on keeping the baby. A woman my mom works with and her husband are interested in adopting and we’d like to handle the adoption privately and without involving the court. I researched NY adoptions online and it seems that no matter what type of adoption you do, you have to go to court at some point. Is there a way around this and can the couple and I just do this on our own? If we do need a lawyer to draft the adoption paperwork, the couple is willing to pay the legal fees for everything.