Electric vehicles are powered by banked potential energy (chemicals stored in the battery). The motors have almost instant access to this power at all times as the conversion to power is very efficient.
Combustion engines have no bank of power to draw from so readily or instantaneously and make their power far less efficiently.
Edit: Stripped the answer a little bit too far back to bare bones, thanks for the corrections in the thread. Not strictly true on the stored energy comment about the battery. They store potential energy in the form of chemicals and a reaction does still have to take place but it is far more efficient and far far quicker than a combustion engine which is having to overcome many more physics hurdles like the inertia of the engine itself, being unable to just go from 0rpm to 5000rpm almost instantaneously to generate its reaction resulting in fuel becoming power etc.
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