Questions about cosmology

Cosmologists today believe that ordinary matter—the kind of matter we interact with every day—is just a small part of the universe.
Most scientists agree that dark energy and dark matter make up a huge percentage of the universe.
In this theory, dark energy makes up more than two thirds of the universe.

How does Big Bang cosmology solve this problem?

The big bang cosmology solves this, mainly by the implied age of the universe.
We only see light emitted within the last 12 billion years (or whatever the age of the universe might be).
This is a long time, but certainly not infinite, and not enough to make the night sky bright.