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.

[Smaay]

nope no cold start injector on the 5S-FE.

sometime I can hear the pump and sometimes I cant. the design of the circuit opening relay is when you turn the key to the on position it sends power to the fuel pump relay, but the signal FC from the ECU is what activated the relay to send power to the fuel pump.

does this make sense? put a meter on the the COR and check voltages