Fuel pump or ignition problem?

What is your question?

Starts normal when cold, after shutting off and trying to restart will crank normal but then die. Only happens after the car was on recently. From research ive done its one of those two possibly a sensor though. Havent checked for trouble codes but no CEL on. Runs and drives normal otherwise.

What makes this problem better or worse?

Giving gas pedal pressure when starting second time keeps it on.

How long has your 2004 Nissan Maxima had this problem?

Just got car so no idea.