there could be a dozen reasons .
Is it a cold start or is the engine warmed up?
Is there an ecu fault indication on your dash console?
Is the car serviced regularly?
answer these questions and i will answer your first question.
It could be a leaking non return valve in the fuel pump assembly, that means the fuel system looses pressure over the period of time when the car is stopped, and then takes a while to repressurise when the car is started again.