This question is about one of the most misunderstood concepts I have run across after many decades of reading science journals.
So if you're like me and get a headache from all that academic stuff from time to time, I am presenting this letter as a playful mind game strictly for your amusement!
From Quora: If the Universe is supposed to be 13.7 Billion years old, why then has the James Webb telescope discovered a Galaxy that is 32 billion light years away?
A: Patience, young pup! James Webb Space Telescope is not online yet. July 12th is the date when it starts to deliver.
You seem to be referring to GN-z11, or some other ultra-deep field discovery. GN-z11 was discovered using a collection of observatories: Hubble Space Telescope, Spitzer Space Telescope, Chandra X-Ray Observatory, XMM-Newton, and Herschel Space Observatory. In that data, the galaxy GN-z11 was found.
GN-z11 is the red blob. That’s as good image as we can get.
Q: That means that the light would have traveled for much longer than the age of the universe!
A: You are missing one crucial detail: space expands.
It works a bit like this: imagine holding a rubberband between your hands.
So perhaps James Webb can take another look at GN-z11, and with the magic of shifting the colours in post-processing to compensate for the redshift, the image it takes may look a bit like this:
But alas, that is just an artist’s conception of GN-z11, and not the real thing.
So again, patience, young pup!