It's not meant to be literal. Rather, it's both a historical and, more importantly, religious reference that gained massive popularity in the 19th century. It is effectively a term for a utopia-esque society, a paradise on earth.

In German, the term "tausendjähriges Reich", meaning thousand year empire, originates with millenarism, meaning a specifically Christian origin that revolved philosophically, theologically, and in terms of art history around the idea of Jesus returning as the Messiah before the end of the world and establishing an empire under his rule on earth that would last for a thousand years.

While the term itself is not specifically written as such in the Bible, it comes from a specific reading of the book of revelations and was highly popular among groups and sects focused on a sort of eschatological Messianism, meaning people who want to specifically work or pray towards an end of the world by initiating the return of Jesus as the Messiah for the second time. From this reading of revelations, there is a period of time when Jesus rules on earth, for – as the lating term milleniarism implies – a thousand years.

The way the Nazis used this however, is not in this sense and not in a strictly religious sense. The way they use it is as a sort of message and metaphor for the idea that an apocalyptic event of confaltion of events would lead towards a complete transformation of society where from the ashes of the old world, a new, utopian and paradisic world would be born.

This usage and idea gained massive popularity during the 19th century – both in a religious and in a cultural sense. In a religious way we see this taking hold within the various specific theologies that originiated in the 19th century that were – and sometimes still are – obsessed with the book of revelations, the apocalypse and the end of the world. The Seven-Day-Adventists, Witnesses of Jehovah and the Mormons can all be somewhat classified as to a certain extent milleniarist while there were many more that by now are dead and/or forgotten.

But there was a lot of bleedover of the kind of metaphor and the kind of thinking – the obsession with a violent conflagration of events that woiuld lead to a "cleansing" and to a new world rising from the ashes akin to a Phoenix – into political movements and ideological considerations of the 19th century.

The Nazi obsession with the occult has become a stereotype/meme thanks to Indiana Jones and various other cultural products but it accords to historical reality that there was a considerable influence of 19th century esoteric and spiritualist movements that can be desicribed as occult. This is where the swastika came from and where the term of the thousand year Reich originated. The most influental esoteric movement on the Nazis was called Ariosophie.

Ariosophie was basically pioneered by Austrian anti-Semite Jörg Lanz von Liebenfels who basically formulated a dualistic religion based on a race principle. Part of this came from the general popularity of esoteric stuff in the late 19th century (the mysterious orient trope etc.) and part of it came from the rejection of völkisch nationalists of Christianity as an invention of Judaism and especially in the case of Catholicism as a force of "internationalism".

This specific strand of esoteric völkisch ideology mixed a theory of the "Aryan race" as the purest and truest of all races with elements from astrology, mysticism, graphology, and pseudo-Buddishm stuff (the swastika as a symbol of völkisch ideology comes from this specific strand of thought).

This line of thought was very influential in the case of some Nazis, especially Heinrich Himmler, Alfred Rosenberg, and Rudolf Hess were fans of the idea of Ariosophy that there once was a golden age where the pure Aryan race ruled the world and that only was destroyed when races started to mix and superiority of the Aryans was question. Especially with Himmler, the idea of a sort of "racial avant-garde" which would fight as a cult-like "convenant of the most racially pure" for the return of this time. This influenced some of the aesthetics and more weird practices of the SS such as their special wedding ceremony or their children naming ceremony which involved elements from what Himmler imagined as old Germanic tradition and which would also easily fall today under occult practices.

Hitler himself was not the biggest fan of the occult. As he said in his tabletalks once, all the occult stuff was nonsense. While he had read Liebenfels and some others, he was not very interested in the occult and considered all the stuff the SS did as not politically helpful. But he was aware of the power of metaphor and terms like "The thousand year Reich".

People had already experienced the First World War at this point and thus experienced an event that can be classified as apoclyptic and that overthrew everything they knew and completely transformed society. Only in the mind of adherents to the Nazi creed, it transformed society to the worse. And thus, it needed another event of similiar scale and proportion that would lead to what they considered paradise on earth.

This is the specific background for the term of the thousand year Reich – it's not literal, it's an established political term of their time.