I think for simualtion purposes, your input should not be a DC source, rather a Vpulse that would step from 0 to the required supply value and get held to this value. In this case, you can accurately estimate the delay between the time of applying the DC source to the time the output would respond. If you use a DC source at the input, cadence (or spectre) will (usually) start calculating the transient initial state from the dc solution, which is usually the circuit's final steady state and you'd never see the delay. So, by using Vpulse you'll force a different initial state and can see the delay.