Could be,
a plugged fuel filter,
a damaged catalytic converter,
If your 2003 Grand Am accelerates without pressing the gas pedal, the throttle plate may be stuck.
A person pressing the gas pedal.
what kind of car is it
If the engine is running it is burning fuel, whether the gas pedal is pressed or not.
Pressing on the gas pedal sends more gas to the combustion chamber for the combustion process which sends more pressure to the engine for your car to pick up speed.
kick down cable is stuck
it depends on how hard your pressing the gas pedal
Maybe you arn't pressing the gas pedal?
Yes, it sure can.
Many cars require you to press the gas pedal when starting the car. It's quite normal.
Try pressing on the gas pedal with more force.
On cars with a carburetor you must press on the gas pedal to activate the choke, cars with fuel injection do not have a choke so this is not necessary.