A plunger should not be the first choice with a clogged toilet. Pour a bucket of hot water in the bowl (without flushing normally).
You can dump in more water much faster than normal flushing without the risk of overflowing. The hot water and fast pour help stir things up while the extra water pushes everything down the drain.
I can use a plunger and knock a turd loose in less than 10 seconds. Getting a bucket and filling it with hot water is at least a few minutes of effort.