The term "mythology" means different things for different people and when it is applied worldwide the problem is magnified. I'm adding to this (in a separate answer) an excerpt dealing with definitions from a book of mine. I'm proceeding here with the idea that you are asking about the classic mythologies of the ancient Mediterranean - the most famous mythologies in the English-speaking world.

The stories recorded, now called "mythology", of Greece, Rome, and even Egypt represent a broad spectrum of narratives that were taken and adapted from contemporary oral tradition. This source apparently included narratives not unlike what was recorded in the nineteenth century from European storytellers: folktales (stories told as fiction) and legends (stories told generally to be believed).

Let's consider the legends first: this genre of stories includes many subcategories, including historical legends - narratives about historical or quasi-historical characters, set in what seems to be a knowable past. These stories are more or less (often less!) based on real events or characters. These stories were often regarded as history and they were told for inspiration and to offer behavior to be emulated. A counterpart of this would be the story of young George Washington chopping down a cherry tree and then admitting the crime because his character was so resolute that he was physiologically unable to tell a lie. Washington was a real historical character, but the incident is fiction; nevertheless, the story was/is told to be believed as an example of how a "good boy" should behave.

Other legend-based involve a primordial past of the gods and the origin of things. These narratives are akin to what folklorists collected in previous centuries, calling them etiological legends. These were told to be believed, but they are not based on history. At the same time they were not "made up stories" as you indicate.

These narratives about the origin of the world, humanity, and all things, stories about powerful supernatural beings struggling with one another and setting our world in motion, were traditional, passed on from generation to generation. It is unclear how or when they originated, but they burst on the historical scene fully formed, so it appears that they were part of the oral traditions of these people well before the advent of writing. One can only imagine a prehistoric legacy being passed on over time for thousands of years, mutating - change is a hallmark of oral tradition - but nevertheless being connected from one generation to the next. These stories were not invented by some mastermind who created religion: belief is not like that, but exactly how these stories and beliefs formed is so remote in a prehistoric past that we cannot easily imagine it.

Since all (or at least most) societies tell something like the folktale - fictional narratives told for entertainment - one can imagine that these types of stories were also told in the ancient world. Indeed, folklorists spent decades with a parlor game of chasing examples in ancient literature of pre-modern folktales in their collections. Corresponding stories can be found, but it is not always clear whether the oral prototype in the ancient cultures were told to be believed or were told as fiction. The distinction may not have been clear in the ancient world, and admittedly, in pre-industrial European cultures - the subject of intense research by folklorists - the "folk" themselves sometimes allowed narratives to slip between the believed and the fictional, so things were far more fluid than rigid definitions might imply.

So in short: some stories in the ancient mythologies were put forward as history and were more or less based on historical events. Some other the narratives were told to be believed, but they were about a primordial past and the origin of things - a setting that was not historical. Some stories may have been told as fiction. Many of these stories of each of these categories had deep roots in prehistory so their origin is unknowable, but it does not appear that they were simply "made up" but rather that they evolved and changed over time.