Babysitter. Seriously just because it is probably in the best interest of the child not to meet you as her mom's romantic partner doesn't mean you can't meet the child, how many parents mom's and dad's have introduced SO'd to their kids as "my friend so and so" hang at the park go to coffee, or lunch at a kid friendly place where the kid will be involved in doing things you get to see your gf and see what the kid is like without the relationship aspect. My kids were pretty fresh still to the divorce when they met my now SO as my friend in a group setting with lots of families and kids of all ages, at the time we were "just friends" and frequently hung out with the same people who my kids knew and hung out with their kids. So when I asked how they would feel about us dating they already had a good idea who he was and what he was like and were all for it.
All else fails help your gf find a babysitter.

Sir, you probably won't like my answer but it's what I think. Most of us started out head over heels in love with our spouses and married them despite the challenges of a stepchild situation. In even the good situations there'll be some issues but with effort from both Parents, life for the Step parent should be manageable overall. It would help to know how long you were dating and how often you saw each other before the children came along.

First, I'm really wondering a few things:
Why didn't your girlfriend have custody of her child initially?
Is the Father fighting her for custody again?
Does he have visitation?
How did she get legal adoption of her niece considering she had some custody issues in progress or to resolve as well?
How fast did this all happen?

Do you have any confirmation besides her that any of this is happening as she says it is? Meaning did you accompany her to any of the court hearings, ever meet ANY of the parties involved, see any lawyer things, etc? Do you know for sure the father or SM was charged with anything? Abuse so bad that therapy and immediate full custody was granted, it seems like the kind of thing that would result in charges. Usually if the Courts for whatever reason deemed your girlfriend not able to have full custody and the Father is involved in some abuse, a middle ground until things are sorted out, would be a Foster situation. Bad deal but a bad Dad doesn't automatically mean she's suddenly a Good Mom. The Courts try not do to the "lesser of two evils" -children deserve better than that.

I'm not necessarily doubting your girlfriends story and maybe this is the Cliff Note -very cliffnote- version but there's a lot happening here that is odd and could spell DRAMA and you don't want any parts of that, trust me. You military guys are infamous for being snowed over by damsels in distress because you aren't around all the time so you trust blindly and you have a natural rescue nature (thank God for that, thanks for your service!) But that can lead to a disastrous love life all too often. Bad choices in women and such...

With all of that said, I'll take you at face value and say, you're starting out with odds against you because the situation is NOT good. There's a child with some kind of emotional trauma from possible abuse and you have a baby that has been bounced back and forth. This is a lot of her hands and even after you meet, this relationship will continue to be back-burnered for a while. She won't have much help from her Sister or the BioFather if they are in different States and there's likely going to be some ongoing fights, which means stress. If you do get in there and add some stability and then have to go away on duty again, then what? What next?

I know this is all going through your brain with the filter of "you are in love" so it's not going to sound so nice, but nice aside, objectively thinking, this may be a situation in which you step back and watch carefully for a bit. Broken plan here or there is par for the course but constantly broken plans and new levels of chaos just kind of piles up to be a situation that may not be best for you. Tread carefully.