I wouldn't say give up but I would say is step back and give everyone breathing room and time to adjust.
You are dealing with the property of the United States Government and what they want him to do. Your needs, wants, desires, wishes for him all come after that. The best foot would be for you to go on your merry way and plan for a single life with this child so that you would/will not be disappointed. It is possible that the child will get medical coverage after paternity is settled.
As a poster mentioned he maybe getting back with the girlfriend who he broke up with (sometimes this happens when people deploy they fight before they leave). There are just so many variables that it would be hard to pick one.
Also you have a mom that has just seen her son off to war and now the news of an unexpected grandchild. That is a lot to take in in a very short time. I know about this and it takes a bit to get over it and to come around (have my own similar personal experience). Wait out the time as requested before you contact his mom as nothing more is going to come of it right now.
Stress is not good for baby so stop. Just make up a baby book for the baby and if dad should want to see it he can. But I wouldn't expect much from him in this situation. He may just be a donor and have no interest. It won't be the first time and it won't the the last time this happens with military situations. Just the next time you have sex use/do something to keep this from happening again.
Sorry to be so blunt but this is a curve ball in life that no one was anticipating that happened. Now you (the family) have to make the best of it.
The other S.
Retired Military Wife
PS May you have a safe and healthy delivery.