Maybe. Maybe not. And if they did, he might have thought that she, or they, were funning him. As others have pointed out, a Facebook post is nothing approaching genuine legal notice.
Well, he maybe entitled for damages, I have said that (she should have served him notification) but if I were the judge, I would not be ruling so fast to give up the child to him; unless I studied both history and backgrounds of both parties. He is not very responsible at 20 years old to have a 3 month casual relationship with a woman he met on fb and doesn’t try to keep in touch. She carried the baby for 9 months. He didn’t text or call her..