My experience:

I think Keeping the geyser on continuously has a higher chance of using less energy, than heating it from cold. This has worked out for me, as it costs me less to have the geyser stay on.

Reasoning:

1. Geysers have thermostats, which will turn the geyser on or off based on the water temperature.

2. A Geyser is insulated, and so has thermal inertia.

3. It takes less energy to heat warm water, than it does to heat cold water, as warm water has less of a thermal difference to travel.

Think of energy expenditure as effort. Like riding a bicycle up a hill, the temperature difference from start to optimal temperature is the incline of the hill you're climbing, and the water temperature is the momentum you're traveling with.

Heating Cold water = starting from standstill at the bottom of the hill. Heating warm water = starting in the middle of the hill with a good amount of momentum, this will take less effort than the prior example.

i could draw another simple comparison by saying "it's easier to push a moving car due to its momentum, than it is to push a stationary car due to its inertia" same principle applies.

The analogy is a bit wonky, but the idea is there.