Obviously this is a very complex issue that we cannot argue on this forum.
People who have examined it in depth would present a better argument...
https://answersingenesis.org/astronomy/starlight/does-distant-starlight-prove-the-universe-is-old/
Argument #1: Speed-of-Light Decay (aka CDK)
There are literally a dozen different ways to time the speed of light that do not depend on atomic clocks, including the ability to measure the energy--and therefore the speed--of photons at their point-of-origin no matter how far away.
But there's another much simpler response: E=MC^2. If the speed of light were different in the distant past, we would be able to detect the dramatic (square-function) changes in energy output and/or mass in distant stars. For that matter, even a small increase in C would have resulted in the incineration of Adam by our own sun.
Argument #2: Time on earth might pass at a dramatically different rate than the rest of the universe
This is basically just a play on Humphries White Hole Cosmology, which I addressed back in post #56. There are a number of problems with this view that are addressed in the article I linked to, but I'll focus on just one:
Earth is not the center of our local galaxy, which we know is well over a mere 6000 light-years in diameter. To have the kind of effect that YEC demands, you'd have to have the galaxy rotating around the earth, not the other way around. Morever, we've observed active events like supernovas in our own galaxy at a distance of over 20,000 lightyears, so that invalidates the whole raison d'etre of the theory.
Argument #3: Assumptions of Synchronization
This doesn't actually make a difference, since nobody is arguing about how old the universe would seem to be to a photon, and the relative speeds of the galaxies to each other can be measured via red-shift. Moreover, there are certain types of supernovae that have a very distinct time-line in terms of their energy outputs that we use as universal clocks to measure the relative speed of time in distant galaxies.
So it's true that different parts of the universe have different ages. It's also true that thanks to the finite speed of light, we can watch the whole history of the universe right back to when the light first separated from the darkness--and that history is far older than 6000 years in our local time.
Argument #4: The Assumption of Naturalism
It doesn't take naturalistic assumptions to look up, take measurements, and realize quickly that there's no way for the light to have reached us in a mere 6000 years. This argument is just a scare-tactic by the YEC crowd: "If you believe in an old universe, you don't believe in God!" That's utter nonsense.
Argument #5: The visible universe is larger in radius than the age of the universe
Already addressed. The continued stretching out of space-time provides a sufficient mechanic to explain this when the difference is 15-17 billion light-years to 13.8 billion years. It is insufficient to explain seeing 15 billion light-years in 6000 years--the speed at which the universe would have to expand would actually rip the atoms to shreds and nothing could ever form.
As I've said in another post, the problem is not the Bible vs. Science, the problem is an interpretation of the Bible based only on its English translation vs. virtually everything we can observe around us. Those with an ability to read the original Hebrew and understand how it's just plain different from English (very different tenses, for example, which actually resolves the Day 4 problem) generally have no problem at all with an old universe.
To put it another way, the Hebrew can be read in a YEC way and an OEC way equally well. Why not then use the information God has made available to us in his other direct creation--the universe itself--to break the tie?
Shalom