system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How can scientists prove the big bang if it happened 13.7 billion years ago?

And how did they come up with 13.7 billion years as opposed to 14.7 billion or 12.7?
gpt
The basic premise relies on the fact is that light and other electromagnetic waves have a travel time, its just that they move really really fast.

By turning our telescopes to the parts of space that are both empty and very very VERY far away we can then "listen" to electromagnetic waves (like static on your TV). The big bang itself created a kind of "cosmic background radiation" which is a fancy way of saying that it's static exists everywhere.

We can then make a guess at the age by knowing how far that point we are listening is away from us and by how fast light can travel. This is not a perfect system but it is mathematically correct (hence why its 13.7 billion years instead of an exact number like 13,726,432 years. We can only be accurate to within 0.05 billion years.)

Thus we look for areas that are the furthest away that we can hear the cosmic background radiation. Because that radiation from that area of space still has to travel to us we can guess its age.

As an interesting point this holds true when looking at planets. Whenever you look at something you are actually viewing it in the past because light, again, has a travel time. Thus whenever a scientist finds a new planet and says something like "It is 40 light years away from us." what this means is that we are viewing the planet as it was 40 years ago because it took light 40 years to travel from that planet to our eyes. Because of this any alien looking at earth from, say, 77 light years away, would be watching WWII, and an alien looking at earth from about 65.5 million light years away would be watching a meteor smashing into a planet full of dinosaurs.