But the Big Bang didn’t happen in the same way as an inflating balloon. Your premise is false. The expansion happened everywhere. That is, each measurable point in space grew (and continues to grow) further from all other points in space. This is called inflation and expansion.

Edit: I should add that for this reason, every point is the centre of the universe relative to all other points. If you were able to teleport to the edge of our observable universe, you’d be at the centre of a similarly-sized observable universe “bubble.”