Start from an observation that the night is dark, and deduce in logical steps, that the universe is expanding.

Answer 1

You are referring to Olbers' Paradox.
The night sky is dark. Yet in every direction we look sooner or later we will see a star, so the night sky should be a solid mass of starlight. This is what would happen in a static universe (one not expanding)
From this it follows that the universe is either contracting or expanding, and if it were contracting the brightening would be even more extreme, so it must be expanding.

(Note: I know I haven't stated Olbers' Paradox precisely correctly, but that is the gist of it. You could probably check the web for Olbers' Paradox and get more info.)

Answer 2

No can do, because the darkness of the night is not the result of the expansion of the universe. The real evidence that the universe is expanding is the red shift of light from distant galaxies. Without that knowledge, which does not come from merely taking not of the fact that night is dark, you cannot know the universe is expanding.

Answer 3

the universe isn't expanding, the Earth and everything on it is shrinking