1. get birth certification the same day in person at your County Vital Record Office.
2. get US passport expeditely
3. you also can get China visa by "express service" the same day in person (you in person, not the baby)
so, you can be ready in a month. however, when the baby is 2 to 4 month old, it is much better time for this stronger baby to travel.
tell airliner you have younge baby with you to reserve the baby basket and baby food.