Space itself expanded, i.e. you should not imagine all the matter piled up in one very dense point somewhere in an otherwise empty universe. The big bang filled

Space itself expanded, i.e. you should not imagine all the matter piled up in one very dense point somewhere in an otherwise empty universe. The big bang filled the entire universe, i.e. was everywhere but everywhere was pretty tiny. Or maybe not, if the universe is really huge or even infinite it could still be infinite or at least very large even after compressing it a lot. You probably shouldn't overthink the story, it is highly speculative and if we are honest we have to admit that we have no idea what really happened. The size of the universe usually refers to the observable universe, i.e. the part of the universe light had enough time to reach us from since the big bang 13.8 billion years ago. That does not mean that the observable universe has a radius of 13.8 billion lightyears but on the order of 45 billion lightyears because the universe expanded during the time the light was on its way. Beyond the visible limit there is probably more universe, but whether it is a thousand, a billion or ten to the hundred times more is hard or even impossible to tell.