What is your alternative if you leave this job? Can you just "go back" to your other job?
If that's the case, I would make sure at least two weeks have gone by and ask to sit down with management and express that "I am enjoying the challenge, making a difference, blah blah blah, however this wasn't exactly what you expected. Had I known it was this, I would have required X to start".
This next part is incredibly important, you then don't say another word. Even if it involves an awkward 5 minute pause. The next person who speaks loses the request.
See what their response is and go from there. You'll know VERY quickly if there is more money available to you or you need to go back to your old employer.