How do I know that this BJT is in the saturation zone without having to simulate it?
Often, you don't know. Experience might help you make a guess, but you are not sure. 

What you will do is make a guess as to what region it is and then try to solve the circuit. See what comes out and if it makes sense. You might find, in the case of a NMOS, that you assumed saturation, but then find a gate-source voltage of just a few tens of mV. You then know that assumption was wrong, and that you should probably re-do the calculations assuming the transistor is in sub-threshold. 

You can itterate like this (which is what something like SPICE or simulink will do) - you assume one thing, do the math, and then update the assumptions (pick models that better fit the regions you seem to be in) and re-do the math, etc...