Why should he have higher ambitions? We've never heard him express a desire to do a particular job (not a realistic one anyway). All he really wants to do is play music, and a higher-pressure job would reduce his opportunity to do that, not increase it. Everything that he's said he wants to change about his life can be achieved as easily or more easily in his current job.
I respect people's choices in life, but realistically, his situation is not tenable long term. The points aren't really touched on in-comic, but we can extrapolate several things:
First, his job isn't secure. As others have pointed out, he only got it because Tai offered it and he will likely only hold it as long as she's employed there. It's questionable as to whether the library needs to pay someone to do what Marten does, or if interns/student workers/volunteers could do it just as well.
Second, he has no room to advance. He does not have a degree in Library Science or anything remotely related, and is, on paper, unqualified to do much of the running of the library. There's no way he would ever be promoted, even if he *does* manage to survive past Tai graduating.
Third, the job is just barely meeting his needs. As others pointed out, he lives frugally and doesn't require much, but that could change at any point, and any major life or medical crisis is going to be catastrophic. He mentioned wiping out his savings and then some to buy the 8-string; it's unknown if the job allows him to save any significant amount, but I doubt it, even with his lifestyle. In addition, he likely has no retirement package or means of investing in one (a serious consideration, even for someone in their 20's), and if he has any kind of health or life insurance with the job (unlikely, but possible), it's going to be the most bare bones package available. As a subset of that, he may be able to subsist on that himself, but if he ever wants a wife or child, he's going to need to seek out more gainful employment to be able to support a family in any meaningful way (I'm aware that his wife could work as well to support a family, and I'm not espousing a 50's housewife view, but if she does work at a more meaningful job with better compensation, resentment is definitely going to grow if Marten were to choose to keep drifting as he has).
Fourth, he's being left behind. I know he has a music degree of some sort, but any other skills/knowledge/certifications he may have gained through college are growing increasingly out of date. The longer he spends drifting in the library, the harder he's going to have to work to catch up if and when he's no longer employed there.
In short, I'm not espousing the view that everyone should be rich or pursue massive goals. People should pursue what makes them happy. But Marten is going to have to realize at some point that even if he just wants to make music and hang out, he needs to strive for at least a little better employment to build and maintain the infrastructure that allows him to chill out and play his guitar. It's hard to relax and play your guitar when you had to sell it to make rent.