[Blakestr]

Piggybacking on this (slight point on semantics but still important in terms of framing the discussion)

Don't tell them, SHOW them. The advice about displaying all of those things, almost like metrics or hitting a benchmarks is key.

There is some obvious psychology at play here - for some bosses it might be more effective to present everything in one fell swoop so you build an ironclad case with no room to argue. Another might be to either build up this proof over a course of a few weeks and mention another point and another project. With deeply held beliefs, it takes time to change one's mind and seems like a rare thing to convert someone instantly. (The question is here, how deeply does the boss believe OP does NOT deserve a promotion)

Another critical point is the company structure and finance. Is there bureaucracy the limiting fact and there simply isn't an open position? Or is the company small enough they can simply make one? To me this would be the biggest obstacle to find a way around/through.