There is a lot of good advice here. It all seems to follow common themes I've found to be true.
As a father of 2.5 and 6mo, I will only add:
1. Don't count on the sleep being just your GF, especially if you're wanting the sleep for a workout the next day. Yes, whoever is staying home tends to take the baby more, and the mom generally has to take the baby more at first, but the mom is so exhausted from being a mom that you need to step up when you can. Whether it's burping the baby or changing the baby or warming a bottle. Do this because it's the right thing to do for your GF, but also for your own sanity. When true sleep deprivation kicks in, especially with the hormones, it can be very trying for a mom, and then you.
2. Be communicative about your training, but also train during the day at school when you can. Whoever said the stuff about "owing her one" is spot on. I was training for a big bike race while our first was 6-9mo old and there definitely was some resentment because it was very hard to do my riding at work or at 4am. Yes I got up and rode the trainer at 4 sometimes, or at 10 at night, but to ride outside meant 5am and that meant missing morning stuff. My wife was much more resentful of that time then when I was just working out, running on the treadmill at work, lifting, etc. during the work day. You have to consider that your GF's body will have changed giving birth and who knows how she will react to that, but one natural and reasonable reaction to that is "how come my BF is out there running, getting in shape, while I am back here watching the kid; it should be the other way around." So, while I think being open about what you need and expect in training is best, the more you can do where it doesnt "leave her with the baby" the better. And definitely give her some time in return, especially on the weekend long run.
3. Expect some strain in the relationship. This is natural. And it's hard. But it will get better. You guys both are doing something you've never done in a sleep deprived environment with no way of knowing if you're doing it right. For us, the first 6mo were a blur and a buzzsaw, but after that we started to come into our own. That's really when the baby started sleeping better. But even with our second, who sleeps better too, we just have less patience with each other. So realize that. And try not to get into a position where running is something else she for which she have less patience with or more resentment towards you.
Good luck with everything. I wasnt training at an elite level but was riding 15 hours a week. It was hard to do but doable. The thing is, you never know how the baby will sleep and you dont know how either of you will react to things. My wife was very postpartum with the first one but not with the second one. Maybe that informs why my post has some negative aspects to it, but I dont mean it that way. It's just really hard if everything goes well, and REALLY hard if there are complications, like sleep, bad postpartum, etc., which are all natural and no one's fault and you cant do anything about them.