I've never fully understood why we can still see galaxies that are 10 billion light years away. The age of the universe is calculated to be 13.9 billion years old and we live on a planet that it is roughly 4 billion years old. The universe came into existence 13.9 billion years ago and expanded incredibly quickly but those galaxies that were created in those early years are still visible to us via the amazing Hubble telescope (see the latest from Hubble). Those galaxies would surely have long gone so why can we still see the light from so long ago? How can we see further and further back to the beginning of the universe because surely the light from the moment of the big bang and subsequent eons would have past by us long ago?
Those galaxies were 10 billion light years away from Earth. So light would take much more time to reach here and that light which is now 10 billion years older can be seen now. Even light from the Sun takes 8 minutes to reach to us. So if somehow sun disappears suddenly(very unlikely) we wouldn't know for 8 minutes.
How can we see further and further back to the beginning of the universe because surely the light from the moment of the big bang and subsequent eons would have past by us long ago?
A simple intuitive way to understand that part of your question: Bigbang happened everywhere, in all of space. As time passes we see more distant parts of the bigbang, or rather, of the microwave background which is the furthest away phenomena we can see. The bigbang as it happened for example 1 billion years ago has passed by us long ago. Today we see the bigbang as it happened 13.8 billion years ago.
We can't see how those galaxies look right now. If a galaxy appears to be 10 billion light years away, that also means that the light took 10 billion years to reach us. It's a bit confusing that "distance" and "time" are sometimes the same thing in astronomy.
So the light which the galaxies emit today (if they still exist) will reach us in another 10 billion years. What we see right now is light that was emitted 10 billion years in the past.
This also means that by looking at the farthest possible distance, we can see light which was created shortly after the big bang. One such source of light is the ubiquitous background radiation which was probably created by the big bang itself. It's easy to see because it fills all the gaps between the celestial objects.
Unfortunately, this also means that we always get an "outdated" view of the universe. If aliens started to blowing stars at the far side of our galaxy, it would take us 100'000 years to see the light.