Reddit mentions of Theory of the Novel: A Historical Approach

It depends on what you mean by "fiction book." Different societies in different places developed their literary styles differently, so there's cases of history and myth being mixed together, or myth used as history, i.e. not held as fiction. Epic poems like the Iliad or Gilgamesh easily date back into antiquity and prehistory. Examples of long-form prose fiction can be found from Rome and Asia as early as the second century CE.

If you're asking more specifically about novels, it's a somewhat complicated question, as literary academia has something of a debate regarding a consensus definition on what actually constitutes a novel. However, the one I've always essentially been taught is: a fictional prose narrative of substantial length chronicling aspects of the history and life or lives of a character or characters, examining the ways in which they experience the world and the ways in which their experiences change them or fail to change them.

Assuming this definition of the novel, the generally held strongest contender is "The Tale of Genji" by Murasaki Shikibu, written in the early 11th century CE. It follows the life of Genji, a son of the Japanese emperor who is disinherited by his father and his subsequent struggle to return to honour and prominence, with a heavy focus on his romantic exploits along the way. The wiki article has a more detailed plot synopsis, and it has been translated into English several times, so it's fairly easily available in bookstores or online (if you do intend to actually read it, however, I recommend getting a version with annotations and historical background like the Penguin Classics version. It is extremely complicated to read out of its context without scholarly assistance).

There are other important entries to the development of the novel, especially from the European perspective. Beowulf (~8th century CE) and Sir Gawain and the Green Knight (14th century CE) are both important forerunners, to say nothing of the myriad of romantic novellas that can became popular around the start of the 12th century and remained so for several centuries, but in particular, Don Quixote (1605CE, mentally unstable country gentleman rides around with his "squire" in pursuit of the glory and adventure of the tales of chivalry he reads) is considered the first European novel, and Robinson Crusoe (1719, the classic castaway story) the first English-language novel.

This answer is a very, very cursory overview of a broad field that touches on both literary and historical studies. I've focused on the novel generally here as its the medium I'm best equipped to speak to, but bear in mind that there are a lot of ways to interpret this question. The first pieces of fiction committed to paper are truly ancient. Even discounting poetry, prose fiction has a long and rich tradition that predates the concept of books (as does arguably the Tale of Gengi). This answer is also formed largely from course notes, but I'll recommend you some sources for digging more deeply into the topic.

• The Novel: An Alternative History, Beginnings to 1600 by Steven Moore. Start here. This is an absolutely exhaustive discussion of the various genres and works of literature from around the world that contributed to the literary development of the modern novel. He covers everything I have in much greater depth, as well as the vastness that I haven't. Also check out this article he wrote for the Guardian around the time of the books publication. It gives a good sense of where his focus is and the scope of his undertaking, as well as serving as an interesting introduction to the world before the novel.
  
  
• Theory of the Novel: A Historical Approach by Michael McKeon, editor. An anthology of literary thinkers on, as the title suggests, theory of the novel. This is definitely more literature-focused, it uses guys Northrop Frye and Mikhael Bakhtin - literary critics as opposed to historians - but they do reflect on some of the historical developments of the novel. Definitely Eurocentric, though.
  
  
• The Novel Before the Novel by Arthur Ray Heiserman, editor. You'll probably have to go to a university library for this one. Heiserman collects a variety of essays that are particularly focused on the development of prose fiction before the conventionally held first novels. Like McKeon, he is particularly concerned with Europe and the West, so stick with Moore for anything other.