Nostalgia for the 1950s (or, more accurately, the late '50s and early '60s) was popular during the 1970s and 1980s. The trend largely started with George Lucas's American Graffiti in 1973. Hollywood continued the trend with Happy Days, Grease, Porky's, Back to the Future, and Dirty Dancing.
As mentioned, what's regarded as "the fifties" in a nostalgic sense isn't really the period from 1950 to 1959. It's more the period from about 1955 to 1963 - basically, the period between the introduction of rock 'n' roll and the JFK assassination. The nostalgic appeal of this period largely rested on the idea that it was a "simpler time" before the social tumult of the 1960s, which was seen as having started with the JFK assassination.
As for whether this was the first time people became enamored with an earlier time period, the is answer is definitely no. 1944's Meet Me in St. Louis is a nostalgic look back at the pre-WWI turn-of-the-century era. In the 1930s, Mae West's films traded on nostalgia for the 1890s. And after the French Revolution, some regarded the Ancien Régime with nostalgia, with Talleyrand famously remarking, "those who have not lived in the eighteenth century before the Revolution do not know the sweetness of living."
Actually, fifties nostalgia was bigger in the 1970s than it was in the 1980s. The movie "American Graffiti" was a smash hit and the Television shows, "Happy Days" and to a lesser extent "Laverne & Shirley" were popular hit shows on ABC. Fifties rock acts, like Chuck Berry, had a resurgence to their careers in the mid to late 1970s. This started to taper off, after 1980. Then there is this classic statement by Bill Griffith, in his comic strip "Zippy the Pin Head" who claimed, with a sneer, "The seventies, the only thing that had any cultural value in that decade was fifties nostalgia". Although, it should be pointed out that Bill Griffith loathed Disco music, so his opinion is rather biased. It does show that fifties nostalgia was the first really strong retro culture in the United States.
I'm going to approach this question from the side, because it touches on a super interesting subject but doesn't address it directly.
What many people understand at a sub-conscious level but don't think about much is that there was a revolution in the industrialized world around the late 1960s and early 1970s. There was a dramatic transformation of culture, society, and government. Overall it was not an exceptionally violent revolution, though there was violence, people were killed, and there were several prominent assassinations. Some of that violence and some of those deaths and assassinations were just coincidental, just as some of the violence in a riot that starts off politically motivated may be caused by people seizing an opportunity for mayhem. But much of it was purposeful. There was a considerable array of forces and a considerable amount of effort put forth by sides working toward opposite ends.
The outcome of the revolution was a huge cultural break across that time period. And this is intensely noticeable. There were several movies in the 1980s and early '90s that were set in the '50s, even though in some cases it wasn't that long before. In movies and TV shows such as Back to the Future, The Wonder Years, Stand By Me, and The Sandlot there is an acknowledged throwback to the earlier generation, with some part of the setting being anchored in the (then) present (with narration, for example, or with time travel in the case of Back to the Future). The time differences in those works range from 20 to 30 years. But that was enough to span two very different worlds. In many ways the world of the 1950s and 1960s is of a vastly different character from the world of the 1980s through today. The world of the 1980s feels much closer to our modern world (despite numerous differences, especially in fashion and so forth), despite a similar number of years lying between them. The Wonder Years, for example, is set only 20 years before it aired. A modern show on the same premise would be set in the mid '90s, with the characters watching the early seasons of Friends, Seinfeld, and The Simpsons on TV. That doesn't seem even remotely close to the same differential as '88 to '68. Friends, Seinfeld, and The Simpsons may be dated in parts but 20 year old episodes still feel substantially culturally modern, just as Marty McFly still feels like a more or less modern character. But Ralph Kramden was certainly not considered a modern character in the '80s.
It's that look into a different, and yet fairly recent, era from the present that incites such curiosity and nostalgia about the 1950s. Layered on top of that you have the unique aspects of the '50s, due to the post-war economic boom, the initial globalization of the world, the dawn of the Cold War, the first stages of the computer era, the spaceflight era, the jet era, and so on. You have a distinctly different era that is often considered to be more innocent or at least less developed. This has a natural resonance with the coming of age themes of many of the works I mentioned above.
'50s nostalgia is a bit like following international travel journalism, the culture is different, the music and food is different, the values are different, the technology is different, but everyone speaks English and the city names are familiar.
Neoclassical architecture could be considered "retro" ? That certainly predates 50s retro culture.
Let me go out on a limb and say the 1890s had a mania for Louis XVI and Marie Antoinette - in fact, general ancien regime. But it was mostly an upper class thing. Once Upon a City shows the Byron photos of a powdered-wig ball (and the gents' beards and moustaches look really silly with that) and that was the period to decorate your house in, not to mention Dolly Varden hats and gowns. But it must have gone deeper than this when Godey's Lady's Book reports the end of the fashion for hair powder for dress occasions. GLB was reporting Eastern fashion, yes, but for a Family Circle kind of reader, not even BH&G type. So while I have not seen this reported in any fashion history book, the 1880-some to later 1890s was seriously stepping back to that earlier period.
Perhaps in terms of a subculture, yes. But mainstream fashion was drawing from the late 18th century during most of the 19th century - the reemergence of the pointed waist and fuller skirts in the 1820s started it off, and it continued regularly until the 20th century. While it eventually became a distant memory, at the beginning of the trend the previous period had been within the lifetimes of many.
The mid-1890s were also drawing from the 1820s/1830s with those large, full sleeves and flared skirts - compare a plate from 1834 with a ca. 1895 suit. Later, in the 1910s, inspiration was taken from the 1800s-1810s. Nostalgia in dress is not a new thing. (I'll let someone else talk about nostalgia in fiction, which I know much less about.)