Nope. The universe is infinite, according to the model. We see observe galaxies speeding away from us in every direction - and it seems unlikely that the earth was the exact center of the Big Bang.
Wouldn't it be more accurate to say that everything was at the exact center of the Big Bang? Assuming it started from a singularity (which can't really be known), everything was in the center.
It would. It is not an unanimous conclusion that "stuff" is found everywhere in the universe and that the universe is infinitely big. However, that doesn't necessarily imply a center or an edge.
The universe might be infinite and unbounded.
The universe might be finite and bounded.
The universe might be finite and unbounded.
If the universe is finite and unbounded, we can go back to the ants on a balloon analogy. As expansion continues (and indeed speeds up) the balloon will continue to inflate, for forever. It is not possible to ever make the trip around the balloon to get back to your starting destination due to the expansion of the universe. The universe and spacetime are the 'surface' of the balloon - there is nothing inside of it, the center is not the middle of the balloon, and you cannot tunnel from one side of the balloon through to another. That isn't to say the observable universe is likely to be the extent or even close to the extent of the actual universe - it is likely still just the tiniest of fractions of the actual universe.
We're probably finite and unbounded, and expanding into nothing. As the universe expands, it creates space where it did not exist.
There's other theories that are reasonable, however. Some posit that our universe is a bubble in a true vacuum, and that there could be other bubbles containing other universes. Those theories are largely driven by the theory of inflation, which is the most accepted explanation as to how the universe expanded so far and so quickly in its early stages. (That's not to imply that the bubble multiverse theory is the most accepted explanation, though - just that most theories relating to bubble multiverses stem from looking at vacuum energy)
We probably won't know for certain in our lifetimes. Intelligent lifeforms might never know for certain.