If it is a fuel pressure issue, on most cars (I can't remember now if ours have it or not), there is a tiny valve on the fuel rail, usually covered with a black cap not unlike the valve on your tires. Before you start it, and after it's been sitting a while, unscrew the cap and push down on the valve (and stand back!). Make sure you have a few rags lying around. If gas spurts up fine, then it's not a fuel pressure problem. If it kinda dribbles out, then it is.
A fuel pump would give you problems, BTW, all the time and not just on start up. You would feel lurching and hesitation while the motor is running.
I would be more inclined to say your problem is probably electronic and not mechanical (imo), but unfortunately, it's a process of elimination.
Here's what I would check:
Plugs (did you change them? I didn't see the mileage on your car)
Wires (are they getting sodded in the humidity? Buy a can a wire drier and spray it on)
Wiring connector to your throttle body (is it in snugly? any loose connectors/pins?)
Basically, if you have fuel, then it's either lack of spark or air that's causing this. Spark/fuel/air are controled by sensors, so if you have these three, then it's sensors. You should ask your dealer if the car is throwing any fault codes.