As rjs showed, you can order a transcript that shows that you did not file a tax return.
However, I suspect that is not going to satisfy whoever is asking for it. I suspect their next question would be WHY didn't you file a tax return, and want proof of that.
You could also order a "Wage and Income" Transcript that would show any W-2s, 1099s, etc. that the IRS received for you (in your case, it would show they did NOT receive anything from you). That MIGHT work.
However, in many cases, the best response would be to file a tax return reporting your $0 of income. Then you could show them you filed a tax return.
