Ask HN: Got hired for a position that doesn't exist. How do I leave?

I'm a recent CS graduate from a decent university in the US. It's no CS powerhouse but it's well respected and decently known. I won't name which because I don't want my co-workers to accidentally see this and identify me.

During my last semester we had a guest lecturer in my parallel programming class. He came from a local startup which supposedly created advanced systems to assist the work of other statups.

The engineer from the startup went on and on about how each day there is a challenge and you learn so much. I decided to apply and see what would come out of it.

I went through a very tough series a interviews complete with Python puzzles and whiteboard problems. During these interviews I was reassured the job there was challenging and rewarding. I got a (generous) offer and accepted.

Fast forward to my first day and I ask my team lead what's the project I'll work on and I quickly learn that the challenging work is done in a sister office. I get told that this location mostly does very simple client facing Java Swing applications. I was devastated and almost quit on the spot. I would have if not for the fact that I have very large student debts and can't afford to not work.

Now I've been working there for a month and I've tried everything to get assigned interesting work. It's pretty much impossible since no such work is even done at my location.

How do I get myself out of this? I'm looking for other jobs already. I could omit ‎my current position from my resume but then I'll be forced to reveal it if I get an interviews during regular office hours.

I have a friend who wants to personally refer me to work on his team at Amazon but I don't want to blow the interview. I would practice but at the end of the day I'm so burnt out from boredom and repetitive work that I can barely stay awake.

I know there are no clear cut solutions but I'm interested in hearing from people who had similar experiences.