Cranks but doesn?t start

[JoeBoxer1130]

So I?ve been having an issue where my 2004 Grand Prix cranks but doesn?t start.
The first time it turns ON fine after the engine is cool, but if I turn the engine OFF after it gets up to temp like pump gas for instance, after that the engine just cranks but doesn?t start and I don?t hear the fuel pump prime.
But, after a couple of hours it starts normal like nothing ever happened.
Fuel filter has been changed
Fuel pump still works
Injectors have been cleaned
EGR valve is new
Anyone with the same issue or any tips to resolve I greatly appreciated.

[cheatah faheatah]

No prime is a major clue. Next time it fails to start, open the underhood fuse box, on the wheelwell, on the pulley side of the motor, right behind the battery. then have someone crank it over while you either wiggle or tap on the square relays. One of them is for fuel pump. If it doesn"t fire up try swapping f.p. relay with another one in the same box. Theres 4 or 5 the same in there. Cheap to replace at your local auto parts store.....E

[JoeBoxer1130]

The relays are good and fuses are not blown. I forgot to post that on the first post.

[Texas3]

Fuel pressure sensor ?