Linear regulator operating point over input DC Sweep analysis
Do the sweep from the highest voltage down to the lowest voltage. The simulator will be able to perform the dc operating point analysis correctly because it will use the high voltage rather than zero.

If your simulator won't support that option for a .dc simulation then use a very long transient simulation. Replace the dc voltage source with a PWL (piece-wise linear) source that starts at the maximum voltage then slowly ramps down.