Distances of this sort of thing are not measured directly - what's measured is its red shift, which tells us both how distant it is (very) and how old it is (very). That inference is indirect and depends on the model of cosmology, but the relevant bit of cosmology is relatively uncontentious.

(But if it really was only 13.5 billion light-years from Earth then you'd be right. In fact it's much further away than that.)