For this statement to be true the definition of what one means by our Universe is important. One current hypothesis has the Universe as effectively infinite in size and age, consisting of a multitude of specific universes of which our universe in but one of many [the multi-verse hypothesis]. When we refer to OUR universe we are really referring to the observable universe, or the O-region. This observable universe is encompassed by the Hubble Volume which is a function of our present technological horizon i.e. the limits of our presumed ability to observe our Universe.
The statement that the size and age of our Universe is known is based upon the current hypothesis that it originated from the 'Big Bang', with inflation taking place within the first 10-30 seconds, driven by the false vacuum. The standard calculation in this hypothesis provides an age for out Universe of approximately 14 billion years. Most scientists place the Big Bang at the theory level of knowledge i.e. a scientific fact that is one level below reality itself. Some scientists regard it as still at the hypothesis level i.e. not a scientific fact because they believe that some observations cannot be reconciled with the concept.