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I feel uncomfortable defining the entire universe like a very big room full of stuff moving around and hearing someone asking where is the centre of the room.
Saying well no - imagine inflating a very large balloon super fast - surely it must still have an epicentre - isn't the universe like that?
Let me give you another scenario - you have a sheet of 10 dimensional "paper" crushed by tremendous force and on a spring trigger to explode. Suddenly it expands - so fast that its own 10 dimensional structure ruled its rate of expansion - the physics of relativity didn't apply here and spacetime itself as we know it got defined some where/when during this epoch.
Now at a point things cooled down and got less energetic until relativity phased in as the dormant force shaping the macro universe, and a 3 dimensional spacetime and fourth dimension of time dominated how most of spacetime continues to evolve. But in that first instant spacetime didn't exist, wasn't predominantly 3 dimensional and geometry or field curvature of a higher dimensional reality reigned. So what we have today is a remenant of the creation scenario - it certainly does not have to be 3 dimensional given the anomonally of its birth.
If all spacetime today was 3 dimensional - it would be simple to reconcile relativity with quantum mechanics, or SuSy with string theory or answer what is the topology of of our Universe or is our universe finite or is spacetime fractal not quantised.
Black holes are an interesting example where instead of a singularity at there core according to relativity (and noting relativity doesn't apply below the event horizon) the event horizon may simply be a dimensional transition zone where we move from 4 dimension space-time to a higher lever dimensional spacetime governed by quantum gravity or some other set of forces that dominant higher dimenisonal membranes of existence.
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