It can go the other way. Too much fuel will make the car hard to start until the excess is cleared. Injectors leaking maybe? A dead/dying coolant temp. sensor will do something similar (along with really bad fuel consumption).
Most (all?) EFI has a clear flood mode where if the throttle is held open a substantial fraction of its travel while cranking the injector pulse is reduced or stopped. The purpose is to clear excess fuel through the engine, perhaps due to a faulty CTS or a marginal ignition system not firing. Otherwise throttle input is best actively avoided while starting.
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