ok, idk if it works without a SS# snce I had one. However, I still needed authorization to work (EAD), and all I did was get the permit from school and they accept it without the government authorization when I was 16. You can still try and fill it out I suppose, I mean it worth a try. Worst case is they tell you no and to get the hell out.

I do know this, community colleges hire students without SS#, so you can wait till you graduate HS and try that in another two years. Other than those two options, the dude that commented before me is right, although phrased it terribly, look for small "mom and pop" shops and ask them up front if they are willing to pay cash, no tax.