If you have a deep interest in this question, I highly recommend Steven Moore's The Novel: An Alternative History, Beginnings to 1600, which is the definitive treatment of the novel as a global phenomenon with ancient roots rather than something that arose in England during the Early Modern period. As you have recognized, the history you were taught is quite Eurocentric and not the full picture. Moore's book is a useful corrective to that, and I’m going to be mostly summarizing his argument, as he remains the best source I’m aware of on the question.

Moore's claim is that our very first novels actually arose in Ancient Greece, beginning with the very popular Greek romances. These were long works of prose fiction which often featured thrilling tales of adventure. Moore says that this novel "was an elastic form that made room for interpolated poems, stories within stories, pornography, and parodies, where the realistic and fantastic blend together" (4). So, while these novels in the ancient Mediterranean where not much like the early novels in English (like Daniel Dafoe's Robinson Crusoe and Samuel Richardson's Pamela), they’re not that far off from many postmodern novels we read today.

The genre died out in the Roman West as other forms became popular (particularly various forms of verse) until proto-novels emerged in the Middle Ages as the romance. (Note here that medieval romance is a different beast from the contemporary romance novel, which is also different from the capital-R Romantic movement, which is different from romance in the usual sense.) The medieval romance was generally characterized by a preoccupation with relationships between men and women (particularly forbidden relationships), questing, and displays of chivalry. These works were often written in prose. In fact, in some Romance languages, the word for "novel" is still related to "romance," such as French roman and Italian romanzo.

Simultaneously, there were traditions of prose fiction in other parts of the world. The most famous of these is The Tale of Genji (early 11th century), which was written by a Japanese noblewoman named Murasaki Shikibu. As you can guess, Moore disputes calling Tale of Genji the first novel, but the book is generally recognized as a novel, and both China and Japan have histories of long prose fiction that predate the novel in English.

The history that you were taught in college was likely accurate—as far as the history of the novel in English is concerned. The received, conservative history of the novel says that it developed out of the medieval romance, and the first novel is Don Quixote (1605-1615). Cervantes's work had an influence on English writers, who developed the nascent genre in works such as Aphra Behn's Oroonoko (1688), Robinson Crusoe (1719), and Pamela, Or Virtue Rewarded (1740). That said, if you get a bunch of historians of the novel in a room and ask them what the first novel in English is, they will fight passionately about it.

This is because the answer to the question depends on how we define "novel." Moore uses a very broad definition (and admits as much), which is what allows him to track a wide variety of "novels" across a times and cultures. This definition would not necessarily be agreed on by all scholars of the novel; some are quite narrow in their requirements. I myself tend to favor a broad definition of "novel" because, after all, "poetry" is also a very broad category. Some would argue that Moore is so broad as to be useless, but I think that he gets better to the heart of your question than a narrow definition. You want to know (I assume) whether or not there were long works of prose fiction before Early Modern Europe, not how long works of fiction written in other times and places don’t fit a particular definition of "a novel."

To that end, our conception of what a novel is will of course vary across time and space. If Samuel Richardson could read, say, Ulysses or even something as ordinary to us as Harry Potter, he might not have recognized them as being of the same literary category as his own Pamela and Clarissa. My dad (who teaches courses on the novel) in fact told me he had a lively discussion about whether or not one of the books they read in his class this semester qualifies! The question of what is and is not a novel and what was "first" will likely keep scholars busy for years.

Not to answer the OP s question but I do know for a fact that the works of prose considerable in length existed centuries ago before the first European novel ( including in Rome, Greece and India but not limited to those places ). A literary historian will perhaps be better equipped to answer whether they could be called novels. My follow up question is : did the invention of printing aid the proliferation and popularization of prose literary form?

Edit : grammar

The first/oldest surviving novel was The Tale of Genji, written in 10th century Japan by Murasaki Shikibu, a lady-in-waiting to the empress. We know from surviving diaries of that time, most notably the Sarashina nikki that there were many other novels (referred to as monogatari, "tales") available that apparently have not survived. Reading them was considered a pursuit for young girls, although passages from Murasaki Shikibu's diary seem to imply that her male contemporaries had at least some degree of familiarity with her work. (Chinese poetry and epics were the preferred literary styles for the upper class.)