There's a subtle misunderstanding there, which is rarely made clear in discussions of the Big Bang and the current model of the universe.
Big Bang did not explode to fill the universe. Matter and energy has always filled the entire universe pretty uniformly, but 13+ GYears ago, the universe was very small and its energy density was very high. But it was still completely filled. Our theories combined with our observations don't tell us whether it was infinite or finite, just that whatever it was, it was was very dense and very energetic.
From that point -- what came before, if anything is utterly beyond the current scope of physics and is pure speculation -- space itself started to expand very, very rapidly and since the mass-energy was conserved, the density of mass-energy rapidly decreased. This hasn't stopped, though it has slowed. Our best measurements to date suggest that it will never stop and probably is speeding up some.
When we look at the CMB, we're looking back in time to about 380,000 years after the Big Bang, to the point where the universe had cooled so that it was no longer a plasma and became transparent to light. Prior to that point the plasma was essentially opaque and there is no way to use electromagnetic radiation to see earlier.
We see the CMB 13 GYears away in every direction, but we're not seeing to the "edge" of the universe (if there is one). We're seeing to the most distant point from which light has has time to get to us travelling at lightspeed. So 13 GYears back is 13 GLightyears out. There's stuff (probably stars and planets and galaxies and all the stuff we know and love) further away, but we can't see it because light hasn't had time to get here from there.
Basically, the universe that we can in principle observe is a 26 GLightyear bubble in a much larger universe. (BTW, all these measurements are light-travel distances. When you take GR into account it gets more complicated, but those complications are not critical to this discussion. See Observable Universe, Distance Measures and Comoving and Proper Distances for typically Wikipedian incomplete-and-confusing but still useful articles.)
The one thing based on observation that we can say is that the universe is probably at least ten times the diameter of what we can observe. Assuming General Relativity and assuming that the larger universe is about as homogeneous as what we can see, the fact that we observe our bit of it to be very flat means that the edge or the radius of curvature or whatever makes the whole thing finite has to be at least ten times further away -- otherwise we'd see curvature in our own observable patch of space.
So the problem is that the part of the universe that we can see is observed to be too small a part of the whole shebang to make any kind of estimate of how big the entire universe is. (It's a whole lot like trying to survey an area of a few square miles accurately enough to estimate the size of the Earth. There's so much noise in the measurements due to local topography, that all you can do is say "It's a lot bigger than a few miles.")
Caveat: If I understood you correctly, your question is about the size of the whole universe, not just the visible universe. If I'm wrong, let me know and I'll frantically re-write this!
Note that even the parts which rely on observation necessarily rely on those observations filtered through the lenses of theory. I've tried to use only the parts of cosmology which seem to be solid and to avoid the wild speculation that produces popular science books and TV specials. But it's still quite possible that it will all be overturned as we come to learn more. (I'll be surprised, but that's happened more than once!)
