Unfortunately, the birth of a child is not grounds for early release in the federal or state system. It is one of the most common questions families ask, and the answer is consistently no.
The Bureau of Prisons and state correctional systems do not recognize the birth of a child as a qualifying event for compassionate release or any other early release mechanism. To put it in stark terms, even a woman who is incarcerated and pregnant does not get released to give birth. She delivers in a hospital under guard and returns to the facility. The system's position is that incarceration does not pause for life events, however significant they are.
What he may be able to do, depending on the facility and his status, is request a phone call or video visit around the time of the birth. Some facilities will accommodate that kind of request if it is made through the right channels, typically his case manager or counselor, and if his conduct record supports it. It is not guaranteed, but it is worth asking about well in advance of December.
The best thing both of you can do right now is document everything and stay in close communication. Send photos through InmateAid once the baby arrives so he can have them in his hands. That connection matters more than people realize, for him and for the child.