That said, as an American I find both Tolkien's, and much of the rest of the world's, idea of a past golden age rather difficult to grasp.
Oh my, did you stum a special set of strings, here!
C.S. Lewis offered to solve your mystery pretty explicitly in his writings about ...his writings (I'm sure that great writers are allowed to do that -- it was also about Tolkien's and other writers of truth through "myth").
It has to do (I agree with him) with a great, deep, but often very elusive desire that is still in man's heart as a result of who God made him to be. We desire what was lost when God walked with man (and even when, after the fall, men were much less tainted by the consequences of our iniquity -- Tolken's "high men" are much like antedeluvian man in Genesis).
That desire is of the same cloth as the very thin, fragile hope for the future that we carry from generation to generation, something I noticed very strongly shown during the first movie's flight of Arwen carrying the wounded Frodo in flight, chased by the deadly wraiths. After the fall, God mentioned that the woman's seed (Jesus) would have his heel bruised, but with the smashing of Satan's own head. In Christ, although the way is narrow, hope becomes secure and not fragile, for our return to glory (His glory).
As Paul said, those who by faith, cleave to our true hope are those who long for "a better country."
A very thin reed of hope we have, until we find the one who bore our doom into the depths of our own death -- death we were never supposed to have, the depths of which were prepared only for the Adversary and his fellow fallen angels. But "a bruised reed, he will not break and a smoldering wick he will not snuff out, till he leads justice to victory."
Thankfully, this victory is one we're offered to take part in, this justice having been met in the death (and resurrection) of God made flesh for us.
Something to long for, eh? And quite a better kind of golden age, to come.