To add some background info to the good ideas in the posts above, the fuel injection system requires an input of fuel under high pressure to function properly. If it had to pump up the fuel in the tank every time the car was started, this would be the symptom as it takes some time to reach the needed pressure level, just like it takes time to pump up a bicycle tire with a bike pump. So it has a gadget called a “fuel rail” which stores a small quantity of fuel under a fairly high pressure, even when the engine is turned off. Then every time you are ready to start the car, it has enough fuel already under pressure available to start right up.
What appears to be happening is your fuel rail pressure is leaking down. This can be confirmed by a fuel pressure test. You don’t see any visible gasoline leaks b/c the leak is internal to the system. It is either leaking from the fuel rail back into the gas tank via the fuel pump check valve, or an injector is leaking gasoline into one of the cylinders. Usually it is the former, and the fix is to replace the fuel pump.