I think you might need some fish food or something to provide the food needed for the bacteria.
TO speed up the cycling process, it is better to use a heater for the aquarium first. Which will speed up the bacteria growth. But must remove the heater and let the tank cool down before you add in your newts.
And maybe if you cycle the tank with the filter will be better. Since the filter will also serve as a biological filtering system. It is supposed to host a great amount of nitrifying bacteria as well. Starting them together might be more effecient.
Adding plants will actually slow down the cycling process. But if you want to add it, add it after the tank is cycled and then add the plants. But adding the plant might stir up lot of unhealthy things for newt. So dont add the newts right after the plants are added.
You also need air pump to pump oxygen in the tank so the bacteria can growth.
Therefore, I think that is why just buying the tank and gravel, adding in water and food will not get your tank cycled. There are more things needed.