Nothing else seems to have survived. Not cities, not even mountains. How did the Red Book survive to fall into the Translator's (Tolkien's) hands?
The answer is indeterminate, but the most likely methods of transmission of the Red Book of Westmarch to the present day are (1) preservation of a copy in a sealed tomb or container, and (2) preservation by repeated copying of the manuscript. The latter is the more likely of the two.
In-universe, so far as I know, Tolkien did not state directly where he found a copy. However, in the Prologue to The Lord of the Rings, in "Note on Shire Records", Tolkien wrote that his
account of the end of the Third Age is drawn mainly from the Red Book of Westmarch. That most important source ... was long preserved at Undertowers, the home of the Fairbairns, Warden of the Westmarch. It was in origin Bilbo's private diary, which he took with him to Rivendell. Frodo brought it back to the Shire, together with many loose leaves of notes, and during S.R. 1420-1 he nearly filled its pages with his account of the War. But annexed to it and preserved with it, probably in a single red case, were the three large volumes, bound in red leather, that Bilbo gave to him as a parting gift. To these four volumes there was added in Westmarch a fifth containing commentaries, genealogies, and various other matters concerning the hobbit members of the Fellowship. The original Red Book has not been preserved, but many copies were made, especially of the first volume, for the use of the descendants of the children of Master Samwise. The most important copy ... was kept at Great Smials, but it was written in Gondor, probably at the request of the great-grandson of Peregrin, and completed in S.R. 1592 (F.A. 172). Its southern scribe appended this note: Findegil, King's Writer, finished this work in IV 172. It is an exact copy in all details of the Thain's Book in Minas Tirith. That book was a copy, made at the request of King Elessar, of the Red Book of the Periannath, and was brought to him by the Thain Peregrin when he retired to Gondor in IV 64.
Tolkien went on to discuss more of the history of this book and others preserved in Shire libraries. It all sounds very much like the brief history of manuscripts that often forms part of a translator's introduction to a classical Greek or Roman text. Recall that translating ancient works was part of Tolkien's day job.
Also, please note that Tolkien is specific about the format: The Red Book is a codex with leaves (pages), not a clay tablet.
It is reasonable to extrapolate that the Red Book of Westmarch was preserved in a way similar to those that survived from our own remote past. We know quite a lot about how books survived from classical times. Few of the materials used by the ancients -- clay tablets, parchment, papyrus, paper of various kinds, rarely metal foil -- can last for more than a few hundred years. The Greeks and Romans and medieval Europeans often stored books in wooden boxes or cabinets that helped to prevent damage from insects and rodents. Bound books (codices) replaced scrolls for most purposes only a couple of thousand years ago, though since the Red Book was a codex, the technology of binding must have been forgotten since the Fourth Age. In the humid climate of Europe, most manuscripts that were left untended have presumably succumbed to rot or pests, but there are some rare cases where books that were sealed away tightly, e.g., in a coffin with a dead body, were preserved intact for centuries. In arid Egypt and the Dead Sea region, ancient books have been found not only in tombs, but also in sealed jars, e.g., the famous libraries of Qumran (scrolls) and Nag Hammadi (codices). So one might imagine the Red Book, or a copy of it, being found in a sealed tomb or container.
However, nearly all of the literature we possess from classical times was copied by hand, over and over. Some books, like those of the Bible, are preserved in many copies, though no originals are known to exist. Others, like the poems of Catullus and a mathematical treatise by Archimedes, squeaked through in a single copy. (Catullus' ribald poems are said to have been used to bung a wine barrel.) Most classical literature by far has been lost without a trace, or exists only as a sentence or two that a surviving author quoted. Tolkien, who was a scholar of medieval sagas, apparently imagined the Red Book being preserved by copying over the years, with errors and annotations creeping into the text at each stage.
Given the geologic time required to alter the physical features, or the energy of a cataclysm needed to do the job quicker, I am inclined to go with "divine miracle". Maybe Eru saw to it that the Westmarch was preserved intact until someone stumbled across the right hobbit-hole, thinking it was just another English barrow.