In an infinite universe, which has existed forever, we should not see darkness in the night sky.
Imagine a universe divided into shells, with stars of a single brightness distributed evenly.
If you look at a shell twice as far, each star is only a quarter as bright.
But there are four times as many stars.
So each shell is equally bright.
If you have an infinite number of shells, you end up with infinite brightness.
There are many other possible explanations which have been considered:
-There's too much dust to see the distant stars.
-The Universe has only a finite number of stars.
-The distribution of stars is not uniform. So, for example, there could be an infinity of stars,
but they hide behind one another so that only a finite angular area is subtended by them.
-The Universe is expanding, so distant stars are red-shifted into obscurity.
-The Universe is young. Distant light hasn't even reached us yet.
The big bang theory might solve this by the implied age of the universe.
We only see light emitted since the beginning of the universe.
This is a long time, but certainly not infinite, and not enough to make the night sky