We can make a very general estimate of the age of the universe based on how distant the most distant visible object is.
It is more interesting how we estimate that distance, than it is how we estimate the age...
But before delving into that, a point: EM radiation does not necessarily fade. Only muilti-amplitude EM radiation fades, light neither degrades nor fades at all.
How the distance is estimated is by Redshift. The more redshifted an object is, the more distant it is and this can be calculated on a mathematical scale.