Intriguing question, my noobie friend! Pragmatically speaking, the age of time won't be known until the heat death of the universe, and even then it's debatable if that event signals the "end of time" or if time inexorably marches on.
However, if you ascribe to the view that time is not an irrevocable entity unto itself and only exists because of man's perception of it, i.e. time exists only prima facie and is an artificial measure created by mankind, conceivably one could argue that "the age of time" will be from mankind's first awareness of the passage of time until the inevitable point that Ol' Sol goes red giant on our asses and wipes out humanity.
