Doesn't always start the first try, cranks a long time, can you hear the fuel pump prime when you first hit the key? Options

[VavAlephVav]

Ever since I've had the Celica I have thought that when I hit the key to start it that it takes several seconds of cranking before I get ignition.
lately it's even gotten as bad as not starting on the first try, sometimes not on the second try until it finally starts the third time. but It doesn't always do it, sometimes it starts right up.
I try not to immediately hit the key to start but I like to turn it to ON for a few seconds for the fuel pump to prime before I turn the key to on. But when I do I cannot hear the fuel pump, on most every other
car I've had, chevy, jeep, dodge, mazda, I have always been able to hear the fuel pump make a little wirrrr sound when you first hit the key. especially when I know the pump is right under the back seat not more than 2 feet away from me I figure I should be able to hear it, but I dont'.
I do have a brand new fuel filter, and I run Top Tier gasoline. First, can you guys Hear your fuel pump when you start it up? or is it normal to not hear it?
Do you think this is a fuel pump problem or something else? I do need to take the throttle body off and clean the Idle Air Control and calibrate the TPS. but idk if that effects starting much. maybe its just crap in the fuel pump screen, but I bet it's the 20 year old stock pump and a Denso reman is only $80 on RockAuto and as long as it's so easy to get to I'll replace it anyway.
I'd rather be proactive about something like a fuel pump then have to get stuck somewhere because of it.
I have a 5sfe from a 98+ camry and I don't think it has a cold start injector.

[VavAlephVav]

I've seen a Denso reman for $80 on rock auto, id rather not get stuck because of a really cheap fuel pump
But thanks for validating my suspicion that the fuel pump is not to blame. I'm taking Dynamics in the summer and so I really haven't had time to read more about troubleshooting the EFI.
I have noticed it only does it when the motor is cold, and once its been warmed up I can start it right up.
And I read somewhere that the later model 5sfe doesn't use a cold start injector, which I think is what smay is talking about, but I need to get a better understanding of what is happening when it starts when cold.
Hopefully ill get some more time to figure it out before it completely breaks on me. I do have a factory Toyota PDF for the 5sfe