There are three ways to age the universe. The three easiest involve the expansion of the universe, the burning of the stars, and the abundances of radioactive elements.
From scientific evidence, lots of it...the universe is about 17 billion years old. How?
In billions
Relaxation times of star clusters - more than four
erosion on Mercury, Mars, and the moon - More than four
Star stream interactions in galaxies - more than eight
Expansion of the universe - 15.5 + or - 4.0
color-luminosity fitting - 18. + or - 2.4
nucleochronlogy - 17 + or - 4.0
deuterium abundance and mass density - 19.0 + or -
anthropic principles - 17.0 + or - 7.0
The mean age is about 17 + or - three billion years.
Accepted, but the point is that adairetron8 has defined the question as an epistemological one. That by definition renders all observable evidence moot, because the central question becomes whether or not we can trust observation.
The universe could have been created fifteen minutes ago and all the evidence and our memories planted by unknown parties for unknown reasons. I might actually be a twenty-seven-foot mutant space squid circling the Antares Nebula who has been zapped into thinking he's a five-foot-four male human sitting in a cheap knock-off of an Aeron chair.
You might actually be Angelina Jolie and I might actually be Brad Pitt. So, are you doing anything later?
The short answer is that our senses are the only means we have to comprehend the universe, and the scientific method is the best available method to synthesize those observations, explain past events and predict future events. It does not, and cannot, explain anything to a point of metaphysical certitude. But if I had to guess whether or not the sun would peek over the eastern horizon of my little sliver of Earth tomorrow morning, I know which way I'd bet.