It’s generally accepted that the Romans didn’t think any more seriously about the old Greek myths than we do about, say, Paul Bunyan. Ovid, for example, opened the Metamorphoses by saying “I prate of ancient poets’ monstrous lies”.
I’ve read (an English translation of) The Golden Ass, mentioned by CalMeacham, and I’m not sure why it wouldn’t qualify as a novel. It’s a prose work of fiction that’s longer than a short story (or a novella). What else would it need?
Now, it has been a few years since I’ve read it, and I remember it as being rather episodic, in that the hero bounced around from one encounter to the next, rather than having a tightly crafted plot, so I suppose someone could claim it doesn’t have the “form” of a novel (i.e. beginning, middle, rising action, climax, and whatever else a novel is supposed to have) but I think that would be overly pedantic. There are modern fiction books that don’t have those elements, but no one doubts that they’re novels.
If you want prose fiction, then there are several Ancient Egyptian stories that are the oldest known prose fiction ever written, not mythological stories which fulfilled a sacred purpose, but just secular prose fiction meant to entertain.
The Two Brothers is one such Ancient Egyptian work of fictional literature. It has the plot and character development that are intricate enough to be in the realm of novelhood, even though it’s probably shorter than what we think of as novels. It certainly is much older than any Roman literature.
I am reading A Tale of Genji right now. It is not the first book by far. In the insert leaflet thing it says it is the first book considered a classic. I don’t remember the exact dates but it was written between 900 and 1100 AD or somewhere around that time frame. I am thinking the later time frame.
Contemporary novels around that time frame also include the Icelandic Sagas which are among the earliest pieces of literature written in prose. You see, most early literature was written in poetry rather than prose so it really limits what you are looking for. So, if poetry in the form of fiction is fine I would add my voice into the Epic of Gilgamesh. It is among the oldest, if not the oldest, pieces of literature out there; however, it is written in poetry. It is also a very quick read as I think the paperback version of it is maybe 80 pages (with translator notes even).
You folks have far more knowledge about this stuff than I ever would have expected, by far, of anyone. I am totally impressed. Thanks to everyone for all their help. I am now quite interested in reading nearly all of the works you’ve mentioned.