A rocket does not work because there is "something to push against". Your initial assumption is flawed, so it's normal and expected that you cannot reason about this right now. A rocket works because there are gases that are ignited, looking to expand. This expanding force is applied to the nozzle, hence to the entire body of the rocket, and pushes it in the opposite direction : up

Imagine yourself floating in space with a heavy object held in your hands. Say an anvil. You push the anvil away. This gesture is going to push you back by some amount as well, since the anvil is so heavy. Well the rocket is you, and the burning fuel is the anvil. A rocket is just an object continually jettisoning weight behind it so it can move forward