Why can we see all the way back to 600 million years after the Big Bang? I apologise that what I'm about to ask has probably in some format been discussed before on the site. Like many recent questions here, this is motivated by the James Webb telescope: a relative of mine who did not study physics read that one of the aims of some recent investigations was to see back to light emitted by some of the first stars, some 600 million years after the Big Bang.
They said "how did we get so far away in that first 600 million years that it has then taken 13.2 billion years for the light to catch up with us?". I tried to say something about how due to relativity, time isn't really a universal concept and is instead more local, and obviously I know that light takes time to reach us from a distance so as we look further away we see further back in time, but the actual kernel of the question I realised I couldn't answer.
How could we be so far away to see that light? Is this due to inflation?
 A: The key point is that the Big Bang happened everywhere. (Perhaps it's useful to imagine a huge array of camera flashbulbs filling the entire Universe, all going off at the same time, 13.2 billion years ago, as a model of the remnant light from the Big Bang that you are talking about).
If we could roll back time 13.2 billion years, staying still in space, we would find that there was light being emitted at our location. That light is now (today) 13.2 billion light years away from us$^\star$, and so of course we can't see it. The light that we are observing today, originated from a place very far away from us 13.2 billion years ago. Because the Big Bang happened everywhere, light was also emitted at that very faraway place, 13.2 billion years ago.
There is also light that was emitted closer to us, that has since passed us and that we no longer see; and (we strongly expect) light emitted further away, that has not reached us yet, that we will one day see (if we are still around). There is even light that was emitted at faraway places in the Universe in a direction not pointed toward Earth, that we will never observe, simply because the light is following a trajectory that does not intersect with our telescopes. It may also be possible that the Universe is so vast that there is light emitted from a place so far away that it will never reach us and so we will not detect it, due to the expansion of the Universe (and in particular, due to the accelerated expansion of the Universe).
A related cute story that I heard in grad school: sometimes, you see pictures of the Cosmic Microwave Background Radiation (light from the Big Bang) as a sphere, with Earth at the center. Seeing this, a kid asked "why are we at the center of the Big Bang?" To which the answer is "we aren't -- we are just at the center of what we see from the Big Bang."

$^\star$ This statement isn't actually really right because the Universe is expanding, but to give a more correct number for how far the light is away from us would require a long discussion of distance measures in cosmology. What I really mean is that light has been traveling away from us for 13.2 billion years. You could say it is 13.2 billion light years away in comoving coordinates, with $a=1$ at the time the light was emitted.
