Recently, I started to ponder again with the question of how do we know the age of the universe.
From my research, the answer is something like: "We measure the expansion rate directly with type ia supernovea, and extrapolate it from CMB data, and with that, we calculate when the universe would have size zero according to the expansion history".
But as far as I understand this explantion, we also need to know the current size of the universe independently of the current age of the universe (because we are trying to calculate its age, and if we need the age for the size, we have a circular dependency).
So my question is how do we know the size of the universe? Is it because we know the universe is infinite so we know it's size (although as far as I understand, this would lead to the question of how do we know the distance to the CMB, because we use that distance to prove that the universe is flat, and therfore infinite)? Is it somehow with the friedmann equations and additional parameters we measure with the CMB? Does it has something to do with the size of the visible universe (although as far as I understand, we know it thanks to the combanition of the age of the universe and its expansion rate)? Or do I misunderstand this explanation?