Another Question About Spacetime

If space and time were created during the big bang, as physicists believe, expanding outwards, that would mean that, outside of the universe there would be no space and no time.
If you say that space and time exist outside of the universe then that would mean that space and time didn't come into existence with the big bang, they were already there.
But if you say there is no space outside of the universe that would mean that, if you were to measure the outside of the universe it would have zero dimensions because, outside of the universe there would be no space for any dimensions to exist within.
The outside of the universe could have no width or height because in order to have width or height you need space and there would only be space on the inside of the universe.
Can a 4 dimensional object exist within zero dimensions? Can an object be 4 dimensional inside but zero dimensional outside? Does that make any sense?