The sun is already really big, from our point of view. But that doesn't stop other stars to be a 1000 times bigger. Also are the dimensions we use to measure the size of space part of this universe and they are only valid inside the universe. So outside of our space time words like "big", "small", "long", "short", "early" or "late" have no meaning. Space and time as we know it are the fabric of our universe. If there is an outside, there may be some other kinds of space and time, but nothing that can be compared or have any connection with space and time of the inside. From this point of view, our universe has no size at all, also no age.
But basically there is no outside for anyone being inside a universe. We have our own space-time which contains everything. If there are other space-times, there can't be a way to exchange matter or energy with it, because the matter and energy of our universe need the space and time of our universe to exist.
This also means there is no exchange of information, since information needs matter or energy. Therefore I think the borders of the universe are also the borders of what we can know.