Your Camaro has an electric fuel pump located inside the gas tank. When you initially turn the key to the run position you should hear the fuel pump go on for a few seconds. It doesn't pump when you crank the engine.
Best way to check for fuel pressure is look for the fuel pressure test port located on the fuel log. It will have a cap on it with a valve step core, just like a tire. Usually located on the back side of the intake.
Preferred method is to hook up a fuel gauge to check for pressure. You could also just depress the valve core and see the line is pressurized and fuel comes out.