As planingan describes, strictly speaking that's the water heater, not the shower. Presumably you could keep the heater on for a while, or at least for a few hours will the whole family showers, so that procedure is more of a cold-boot than actual shower operation.

One other thing about Japan is that public baths are very popular, and a lot of people use them not just to relax but for their daily shower/bathing, shaving, and other grooming needs.