Well, there are a number of possibilities that have to be considered. But let's just consider one where the universe wraps back on itself. If the universe wraps back on itself based upon its spatial curvature, then current measurements place the spatial curvature to be within 1% of zero, which makes the radius of curvature at least 10 times the Hubble radius, which is a factor of a few larger than the observable universe.
If the universe is flat but still wraps back on itself, then this induces anisotropies, which we should be able to see in the CMB. But we don't. Thus if it does wrap back on itself, it would have to do that very, very far away (again, a factor of a few times the observable universe).