Ice cubes are formed more quickly from hot water than cold water, especially if the container filled with water is placed on a layer of ice.
The conditions of the experiment, however, are decisive: the metal container must be large enough for the convection to develop, but not too large for the heat to dissipate quickly. The presence of wind (cold air flow as in an industrial cold room) is of great help; hot water melts the ice under the container, improving the thermal contact between the container and the cold surface. The improved heat loss from the container more than compensates for the additional heat to be removed.
The characteristics of the water used will also influence: first, whether from the tap or distilled, it behaves like ice cream; the chemical composition therefore has no influence.
Second, dissolved salts, such as calcium and magnesium carbonates, precipitate if the water is hot, which can be checked by looking inside any electric kettle. Unheated water always contains these salts which, when ice forms, will be discharged to the outside. Their increasing concentration in water that hasn't yet frozen lowers the freezing point, as does the salt spilled on snow in winter. This water must therefore cool down further to freeze. In addition, since the temperature difference is smaller between the liquid and the air, the heat dissipation is slower.
Third, water at 10°C reaches 0°C faster than water at 30°C, which is well predicted by the laws of physics, but subsequently the initially hot water solidifies faster. In fact, the heat loss from the free surface of the water is proportional to the temperature. If the surface is warmer than the rest of the water, heat dissipation is better.
Finally, standing water is a poor conductor of heat: ice forms on the surface and along the edges. If the initial temperature is around 10°C, the core of the liquid cools very slowly, especially if ice floats on the surface, preventing normal convection: the warmer water cannot reach the cold walls, it cannot dissipate its heat. If the initial temperature is 40°C, an intense convection is established before the water freezes, and the temperature at the heart of the liquid decreases quickly. Even if the ice appears later than in the previous experiment, full solidification will be faster.
That said, another variable also comes into play: the temperature variation in the refrigerator. The magnitude of this variation depends on the sensitivity of the temperature sensor and the response time of the control system. Suppose that in a standard freezer temperature the power used has a standard value. If a container of cold water is placed in it, it will not trigger the sensor and will not cause additional energy consumption. A container of hot water, on the other hand, will trigger the sensor and start the cooling system (we observe the same principle in an electric sauna. By deceiving the temperature sensor by spraying it with fresh water, we can considerably increase the sauna temperature).
So you can get ice cubes in fifteen minutes instead of twenty if the cold is enough.