You asked:

How do we know the age of the universe?

Marshall Brain Answered:

Scientists currently estimate the age of the universe to be 13.75 billion years old. This is the number of years that have elapsed since the Big Bang. But how do they determine that number? They do not use a single technique. They use several different techniques, all of which point to approximately the same age. As science advances and techniques become more refined, the estimated age of the universe gets more precise.

We know that the universe cannot be infinitely old – that it had a beginning. If it were infinitely old, thermodynamics tells use that everything should have a uniform temperature. Clearly that is not the case.

The simplest way to calculate the age of the universe is by looking at the redshift of different galaxies, and correlating the redshift with their distance from earth. Scientists can then calculate backwards to a point of origin in time.

Techniques have also been developed using the cosmic background radiation:

The Wilkinson Microwave Anisotropy Probe has made calculations in this realm very accurate:

An interesting lecture that looks at cosmology, “Observing the Origins of the Universe”: