If she's pregnant, "9 weeks" now means she got pregnant around July 2. So, it could be. But it kind of sounds like she is not trustworthy in this story. The "weeks" count starts on the first day of the last period, not at conception.
If they do actually get to a doctor, your ex should ask the doctor if she has had any ultrasounds. She might have been fobbing off someone else's ultrasounds as hers. Your ex should ask the doctor when she might have conceived (not just "how far along is she?" because he will then just be given a weeks count, which doesn't measure from when the person conceived). He needs to use the c-word, conceived. And he should ask the doctor for the estimated due date, calculated from an ultrasound, not counted from the first day of her last period.
Be sure he knows not to leave the doctor without seeing any ultrasounds in her file or having the doctor read them, and getting an estimated due date and/or a doctor's estimate of when conception was.
There is a really expensive DNA test that can be done before the baby is born, it uses a blood draw from the mother's arm and a swab from (I hope both) guys. If she's really pregnant and if she intends to keep the baby, he could offer to pay for it. (Though on the kind of money he's making in boot camp, maybe it's out of reach financially.) Since she might have been sleeping with someone else at the same time as him, a DNA test is going to be needed sooner or later anyway, and if he could afford the costly test he could know in a few weeks from now rather than waiting. (Post-natal DNA tests are much cheaper.)
A lawyer is not going to be able to force the woman to let him go to appointments with her, BTW. But a lawyer might be able to help him get access to her real ultrasound scans (not copies that were sent by her).
In the meantime, get your act together about this guy. He is a cheater and cheaters always cheat. He lied to you also. Forget him for you personally.
Good luck.