Going with the balloon idea, the universe is the surface of the balloon. A sphere doesn't have a center on the surface.

We could say that the center of the sphere is where the big bang started. The distance to the center of the expansion is 13.7 billion years. It doesn't have a distance in x,y,z coordinates, because those are all on the surface, and it's kind of futile to attempt to understand time as a fourth dimension in this regard. We don't know if the universe is spherical at all. It's just a description used to portray the expansion. The expansion is also happening faster than light, which makes it impossible to convert the age of the universe to a size. The universe is bigger 13.7 billion light years, perhaps even infinite. Infinity doesn't have a center either.

The "edge" we see is just the furthest point in the universe that light is able to reach us from. Beyond that the universe is receding too quickly for the light to make it to us. Since the expansion is uniform, we can see an equal distance in all directions and thus we are at the center of our visible universe.

We don't know if spacetime loops around or is infinite or has an expanding boundary. Best we got for reference is the cosmic background radiation, but it doesn't tell us about any center

I don't like the balloon analogy because it suggests a center but everything is moving away from everything else. It's more like infinite balloons being blown up at once which only works because the universe is infinite. It's more an expansion than explosion. That's how I've always conceptualized it anyway but happy to be corrected