How can the system output be dependent on itself, when at the initial state there is no system output? I don't understand how it can work physically.
There will be a system output. Say you're controlling a motor shaft, and the sensor is an encoder that measures the angle of the motor from 0 - 360 degrees. When the system is turned on, the motor shaft has a rotational position, which is measured by the sensor. The motor will then turn to the angular position dictated by the reference signal.
Think of the output as being a state, ie a speed, position, temperature. When the system starts, the output has an initial state. A motor might have zero speed, oven might have ambient temperature.
Depending on the exact circuit, the output either slowly builds up or "jumps" to a certain value as soon as the power is applied.
Maybe your understanding here is that the output's "existence" is dependent on all of the previous blocks, but the reality is that you can have an output on its own without anything else. The rest of the blocks simply provide control or limits for that output.