Thinking on a 2D plane, Is the "point" of the big bang still active?

The analogy of looking at the surface of a cloud isn't bad, but there's a crucial difference: the edge of the cloud is at a particular place, while the edge of the plasma that produced the CMB is at a particular time.

Light travels at a finite speed, so visible objects that are more distant in space (in any direction) are also more distant in time (in the past direction). Therefore it can be hard to tell the difference between a boundary in space and in time. On top of that, every familiar example of a boundary is spatial. So you'll often hear it said (even by me) that the edge of the observable universe is 46 billion light years away, but it's really better to say that it's 13.7 billion years ago.

The origin of the universe is "behind" the CMB surface, but that means it's at an earlier time, not a more distant position – and in particular, it's not at the spatial center of the universe (there isn't any).

That said, it's possible that part of the initial state of the universe, whatever it may be, is outside our past light cone. That would mean that it hasn't unambiguously happened yet (nor unambiguously not happened yet).