They start rolling out the icons at Round 4, which I think I've reached -- but not much further than that, since this game is like a chicken bone with a tiny bit of meat on it.
I'm not sure that any human has gotten the ambulances without savestates! It takes a minimum of 123 rounds completed to get the first of the ambulances, and 138 rounds to get the "CHAMPION" text at Round 139 aka D9.