I want to anlyse large signal model for this circuit.

The condition for M1 OFF is: Vin - Vout < Vth (*)
Here is what I am confused. Because I am trying find the condition for the transistor to be OFF, is it possible to use the OFF state to infer Vout = 0 and
get Vin from (*):
Vin - 0 < Vth or Vin < Vth.
In this case the OFF state is used in finding OFF condition and I am not sure if it is right.

 

Yes, for sure for Vin < Vth NMOS if OFF.

 

As with all multi-region devices, the basic way to determine what region it is operating in is to assume it is in one of those regions, analyze the circuit under that assumption, and then verifying that the analysis results are consistent with the requirements for being in that region.

For instance, let's say that Vth is 2V and Vin is 3V. You assume that the device is off, meaning that no current is flowing in the lower resistor and, hence, Vout=0V. This makes Vgs = 3V which is not consistent with the assumption that the device is off. Therefore the device is not off and the assumption was bad. Pick another region and try again.