Exactly! If you see any video footage of a rocket launch, it is clear that the rocket starts off with almost zero-speed. But, the rocket still makes its way out of the Earth. How?
The rocket's engines are burning so much fuel because they are trying to get the rocket's speed to 11.2 km/s as quickly as possible. If you could launch a rocket at 11.2 km/s straight off the launch pad, you wouldn't need fuel at all. The fuel is required to get the rocket to that speed from the initial speed of 0 km/s.