Is this possible?

I am new here and have a question about "adopting" a baby from the Philippines. First some background: My father was born in the Philippines but has lived and worked in the US since his 20s. He has dual citizenship in the US and the Philippines. He has started several mission projects in the Philippines for which he goes back to oversee about 4 times a year. On his last visit, he and my mom were visiting a clinic in which there was a baby born to a university student which she didn't want. My dad's niece is a nurse at this small clinic and asked my parents if they would be interested in taking the baby - the physician there said he would just sign their names to the birth certificate, no money. This was a year ago. My parents didn't take the baby but the seed was planted in my mom's mind as to how she'd be able to help these babies who are unwanted. Is it possible for my parents to be signed on the birth certificate or another couple who would want a baby? By what process would the baby be able to leave the country and enter the US? I am assuming if my parents were to be on the birth certificate then they would need to go through the adoption process in the US in order to give the baby to someone else. My older sister and I who each have 3 children of our own have interest in taking a baby that's not wanted. Obviously, none of us want to do something that's not legal. Thanks in advance...