how does it start the unit since the contactor is not energized?
how is the complete circuit getting closed/

I know where the wires from the thermostat connect to that panel with the R, Y, W, G, C erminals but I donot undserstand how the whole thing works together

maybe someone could explain it in detail please

TIA p
TIA = thanks in advance

This applies to many, not all, numbers, colors and letters may be different.
Basically you usually have a 240 volt to 24 volt transformer used to control the contactors, one side of the transformer may get power continuously to one side of the contactors, the other side of the transformer goes to the thermostat, usually a red, then when set to cool, it will place power to the green(to activate the Blower) and alco connect the blue or yellow for the compressor contactor.
When set to heat, red at the thermostat connects to the g(green) for fan and to W(White for heat.
When thermostat is set to cool, 24 volts should be at Compressor contactor coil to energize contactor, turning on compressor.