If this was an aviation forum you may have opened a can of worms.
First, you can't see a sonic boom any more than you can see wind or sound. It is just a compressed sound wave.
While the first one is often reported as seeing a plane break the sound barrier, there is some debate over that. The first video is *not* a sonic boom. Depending who you ask, that cone is created as the plane breaks the sound barrier, ie, accelerates from just under the speed of sound to just over. In other-words, the creation of the sonic boom, but not a sonic boom itself. However, some claim that it is not necessarily the case, that can happen in any high speed, high humidity conditions. Conditions have to be right and so it is not a guaranteed event.
But way cool. I would love to hear one, or better yet, make one 😀