What year is yours?
No, believe it or not, not every car has a fuel filter. Example, 1997 Jeep Grand Cherokee. Some may call the "strainer" in the fuel tank a filter, but its not your normal filter that gets maintained.
Anyway, you may have what is called fuel pressure bleed down. When you shut the engine off, fuel is supposed to stay pressurized in the fuel rail. But in some situations the fuel will drain back into the tank. Then when you go to start the engine, it takes longer because the fuel has to fill the line.
Also, some GM cars have a fuel pump relay that fails, GM uses the oil pressure switch as a back up. So when the oil pressure reaches a set amount, the fuel pump gets power.