Is it possible to point to a direction in the sky and say "that way is the center of the universe, where the Big Bang started?" If not, why not?

Our friends in the CATO Rocketry Club in Gales Ferry, Connecticut, wonder whether it is possible to point to a direction in the sky and say "that way is the center of the universe, where the Big Bang started."
The "center of the universe" has always been a very important idea for humans. Just as a new baby might think he or she is at the center of the universe, for thousands of years people saw Earth as the center of the cosmos. Some ancient Greeks thought the universe was made of two spheres: one of the spheres was Earth, and the other was the sky, which surrounded Earth and was studded with stars.
In the 1500s, the Polish astronomer Nicolaus Copernicus had a better idea—although still wrong—for explaining the motion of the planets through the night sky. He thought that the Sun was actually the center of the universe, with Earth and the other planets circling the Sun. However, the sphere of stars surrounding the solar system remained as part of his idea.
Now we know that not only are we humans not at the center of the universe, but there is no center of the universe!
The Big Bang is the name scientists give to the events that started the universe. The Big Bang is often described as a huge explosion. But the problem with that picture is that an explosion has a central point where it starts, such as a bomb or a spark. The Big Bang wasn't like that, but an explosion is the closest thing in our everyday experience to help us understand it.
The Big Bang cannot have happened at a particular place in the universe, because before the Big Bang there was no universe! The Big Bang happened everywhere at once, about 14 billion years ago, bringing space and time into existence. The Big Bang kicked off a rapid expansion of space, and space has been expanding ever since.
If we had a powerful telescope that could see all the way to the end of the universe, would we find more of the universe on one side of Earth than on the other? No. We would find that it looks the same in all directions. So does that mean we are still at the center of the universe? Well, no, it doesn't.
Imagine that you are one of many tiny pencil marks on a balloon. You can see only in a line across the balloon's surface—not into or out of the balloon. No matter which way you look, the end of your world seems to be the same distance from you. But that doesn't mean you are at the center of this little world! If you start moving across the surface of the balloon, it would still look as if you were at the center of the world, but the fact is that your two-dimensional world has no center.
Now, suppose your balloon world is being inflated with air. All the other pencil marks will be getting farther and farther away from you as the balloon gets bigger. In fact, all pencil marks get farther from each other, so no matter where you are, it looks as if you are at the center of the expansion. Although it may be hard to imagine that happening in space, the expansion of our three-dimensional universe is similar. Space itself is curved, so as the universe expands from the Big Bang, it is somewhat like the two-dimensional space on a balloon. But just like the surface of that balloon, there is no center in the universe.
One of the ways scientists know the Big Bang happened is that they have been able to see the faint radiation left over from shortly after this cosmic birth. In a remarkable scientific accomplishment, they predicted what this radiation would look like. Other scientists found the radiation using a special telescope, and as more measurements have been made from Earth and from space, the Big Bang has continued to provide an excellent description of how the universe has evolved.