Just think about this for a minute: The reason why some scientists claim the universe is 15 billion years old is because that's the longest distance they've been able to see out in the universe, meaning then that our planet is in the center of the universe. How likely is that? It's as silly as when they believed the earth was the center of our solar system!
In the video I posted the link to the guy says that the longer the telescope stare out the older the universe seems. It could as well be that the universe has no beginning or end, it just goes on forever. I don't like it when things are taken for granted at the limits of our understanding.
You're very close to understanding this. Indeed, if we look out in every direction, we seem to be at the center of the universe. Far away things are moving away from us (they are all red shifted), as if we were at the center of an explosion (big bang). This motion does not allow for a steady state universe. If we extrapolate the motion, at some point in the distant past, the Earth was at the center of a large explosion (big bang).
That would be quite a coincidence if the Earth was the center of the universe (even an absurd statement to make). So instead of make that conclusion, scientists assume that
every point in the universe is the center of the universe. That is, that the actual space that we're familiar with (meaning the distance between two arbitrarily chosen points) is expanding. From any point in the universe, if you were to look out, it would look like you were at the center of an explosion, because you
are at the center of an explosion. At the beginning with the singularity, all points in space were infinitely close to each other. As the big bang occurred, it wasn't the matter that exploded out, but the space upon which matter sits. And this space is still expanding.
And it's not just a clever idea. It explains why background radiation has "cooled" since the time of the big bang. It's not that it's exchanging heat with an outside universe (as your video claims is obvious), but that the density per unit volume is decreasing, because
space itself is expanding. An expanding universe decreases the pressure of that background radiation, "cooling" it.
That's something of a simplification, but that's the best way to approach the idea.