What does it mean by "the age or our universe"?

Question

I am always puzzled by the notion "the age of our universe" because, correct me if I am mistaken, the universe is the entirety of the spacetime. So how can we measure how much time has the entire spacetime has evolved if the spacetime has already included "all time"? Allow me to use a bad analogy, it is as if, in the pre-relativity sense, asking what is the position of the entire space, if the space has already contained all the possible positions. Such question only make sense if we imagine that the entire space is actually embedded in another, again allow me to create my own term, "hyper-space" so that we can find the "position" of the entire spaces referencing such "hyperspace". That's why I always wants to know what exactly do physicist/mathematicians mean what they use the notion "the age of our universe".