[speedygonzales]

More than likely it's due to a stuck open fuel check valve in the sending unit.

Next cold start (where you would normally encounter the problem) do this. Turn Key On Engine Off for 5 seconds DO NOT CRANK THE ENGINE.
Then turn the key off for a few seconds.
Then do KOEO again for 5 seconds.
Do this process for 6 times
After the 6th time, turn it over like you normally would to start and see if this time it fires up quickly without having to crank it.
If it does now fire up quickly (after having primed the fuel system) that clearly proves the check valve is stuck. The only way to correct the problem that I've ever seen in 20 + years of owning mine is to replace the fuel sending unit.

If that does not change the problem, I guarantee the cap and rotor are the problem.

But for now focus on the culprit being the fuel problem.

As a "never hurts to try" you might consider using a complete fuel system treatment for several fill ups. I have had the stuck check valve problem 2 times in 20+ years of ownership and still to this day don't know what causes it to stick but I'm pretty sure it's not debris since the sock on the pump is a fine mesh. Good luck to you.