Why do scientists maintain that the universe is only 13.8 billion years old even though objects can be observed to be 46 billion light years away?
You will notice that I did not ask why objects can be observed to be 46 billion light years away.
I am asking why scientists maintain that the universe is only 13.8 billion years old.
I would like to take a generic stab at answering related questions to this question.
In 276 BC Eratosthenes calculated the circumference of the Earth to within 1.6%. I know that may not seem impressive to modern day man, but take a step back and really look at what he accomplished. Did he do this by circling the world, by using a satellite, by using extensive maps... No. He did it with math.
In 1786 Edmond Haley predicted the elliptical path of a comet he noticed appeared in two instances of recorded history and predicted it's coming arrival and was right. Again, he did this before satellites and computers, etc.
My point is to show how phenomenal feats of mathematics and science have long been accomplished by man before the technology we take for granted today came into play. The way we have always done it is simple.
You figure out basic mathematical and scientific truths that you have verified via experimentation to the point where you are virtually 100% confident in their validity and then you simply apply those same truths to something else, something bigger or something small or something different... Doesn't really matter because the truth will usually apply.
In the case of figuring out the age and size of the universe, we apply the knowledge we have gained concerning energy, force, electromagnetism, gravity, time, and space and mathematics and we apply that to the things we can observe such as background radiation and related measurements from deep space.
As our understanding of the above subjects improve, we will become more accurate and precise in our predictions and extrapolations.
I think that laymen do not understand or appreciate just how complex upper level science and mathematics has become over the past couple of hundred years and especially within the last 50 years. With the advent of computers and explosion of Moore's law, every scientist and researcher today is essentially equivalent to a team of one thousand 19th century scientists... Today, a scientist can do a complex calculation in seconds in what a century ago would have taken months or even years to do. He can then amend, augment, change, refine, or discount his calculations and start anew...
So in general, the way we figure out the seemingly impossible is just by applying our hard earned knowledge on a grander scale. When it comes to things like the size or age of the universe, we aren't trying to solve that question using protractors and trigonometry. We've moved well passed that and are applying Relativity, Gravitation, Conservation of Energy, and Electromagnetism in a complex equation that involves pretty much every force within the entire umbrella of known physics as well as theories of unproven (unverified) forces and sources of energy and matter.
If I were to hazard a guess, I'd guess we're probably on the right track but a few equations may have a few holes in them that will be shored up as physics progresses. but the methodology and science is sound...