We cannot prove the absence of light in a place that is already so far away that it's light will never reach us. Do you agree? We can prove what we can observe, and from that proof we can make inferences about what we cannot observe.
The entire premise of dating our universe is based on its observed rate of expansion. This was accomplished by extrapolating data from observable light and tracing it back to the so called Big Bang.
I see a lot of problems with this one dimensional assumption, which to me seem really obvious.
First of all, let's assume that we actually got it right this time and accurately traced light back to the Big Bang - how can anyone be sure that it was the first and only Big Bang?
Pangea, the super continent, for instance - many may think of as a single place and time in history, but in fact it's more likely that many Pangea's have come and gone in various states as the planet roils on. There will likely be another in the far future.
Perhaps the Big Bang was merely a "localized" event and there are Big Bangs occuring in distant places whose light will never reach us. Perhaps we have gone through many Big Bang / Big Crunch cycles. We simply cannot prove it one way or the other, and so to take a strong position on this would be unscientific.
More food for thought - imagine that the universe has already been through a near infinite number of Big Bang / Big Crunch cycles, it begs the question, do we reset the clock every time or do we let it run?
In my opinion, currently accepted theory is akin to believing that the Earth is the center of the universe and the sun revolves around us. We were wrong about that too.