How to continuously sample a signal WITHOUT using a trigger?
There must be some kind of trigger to tell the scope to start sampling.

If you want a trigger that isn't correlated with any event in the input signal, traditionally you would trigger off of the 50 or 60 Hz mains supply of the scope. Most scopes have a built in capability to trigger off the mains or "line" voltage.

Other options provided by many or most scopes:


Trigger off of a front panel push-button
Trigger off a remote interface (GPIB or serial) command
Use auto-trigger mode and set the edge trigger level to where the input signal will never cause a synchronized trigger.