I think I'm starting to get the point about the CMB.

If I understand well the CMB that we observe was radiated billions of years ago.

But another civilization at the edge of our observable universe could be looking in our direction "right now" and make the same observation because the image that they would get is equally ancient.

The CMB thus shows us how the universe was like ~14bn years ago since that it the estimated distance to its source.
But if the entire universe is far greater than the observable universe, doesn't that mean that the universe could be much older than 14bn years?
In other words, how do we know that the CMB shows the state of the universe 'soon' after the big bang?