What is needed for a baby born is US but will live in China

The baby needs to apply for Chinese travel document to go back to China with his parents.
Those documents are needed: a fully completed application form, a recently-taken bareheaded color photo, birth certificate, parents’ passports, and valid US visas. Afterwards, submit the application to the embassy of China to apply for the Chinese travel document.

Ok. & what if only the Mom is in the United States. Can she do it herself? Or does the father also have to be present for the baby to get approved for the Chinese Travel documents?

I think you wife can do it alone. You don’t need to be there if it is not required. But you need to provide a power of attorney.