Physicists have shown that the total energy of the universe is zero. Based on this, and with the help of the two theories of relativity, we can show that the universe is spaceless, timeless, and immaterial.
SR has shown that matter and energy are equivalent. If the total energy of the universe is zero, its material content will also be zero. If its material content is zero, then we can say that the universe as a whole is immaterial.
We human beings are not immaterial because the total material content of our physical body is not zero. But the universe is not material. That is because its material content is zero.
Again GR has shown that space, time, and matter are so interlinked that there cannot be any space and time without matter; similarly, there cannot be any matter without space and time. If its material content is zero, its total spacetime will also be zero.
What does it mean that the total spacetime of the universe is zero? It means that the universe as a whole is spaceless and timeless.
We have already seen that the universe as a whole is immaterial. Now we have seen that it is also spaceless and timeless. So, we can say that the universe as a whole is spaceless, timeless, and immaterial.
If the total energy of the universe is zero, then that will mean it was always zero in the past, it is zero at present, and it will always remain zero in the future. That is because we can neither create nor destroy energy.
Therefore the universe as a whole was always spaceless, timeless, and immaterial in the past. It is the same at present and will always remain the same in the future.
That means the universe as a whole does not change at all.
That nicely explains why the wave function of the universe does not contain any time variable.