Yes, I am going to do that and hire a lawyer since everywhere I have read, it seems like I will only get one chance at it. It is expensive but I feel like it is worth it for securing any doubts about my child being a US citizen or not. Thank you for your response. The reason I wanted to know what date to use is because it is required when I apply for a visa for him to visit his birth country. Thanks again.
Also I did not get any letter from the passport office saying they kept his Green Card. I do have copies of it and hope it will be enough for the N-600 application.