The idea that characters, figures, and events of myth and folklore are rooted in people and things that occurred way way back in history is called euhemerism, named for the philosopher Euhemerus of 4th century BCE Greece. And there are a number of euhemeristic explanations for how people developed mythological creatures, such as finding bones of real creatures and building stories around them. /u/itsallfolklore goes into that thought-process and how much it holds up in these answers; they aren't specifically about Cyclopes and elephants (though they will address it at one point or another), but they do speak to the overall logic behind this example:

• What leads to mythical creatures being "created" and why does it happen so often throughout cultures?
• How did dragons come into history, any possibility they found dinosaur bones but assumed dragons?
• From Scandinavian elves, Basque iratxoak to Mayan alux, there seem to be multiple disconnected cultures with a common "little people who live in the woods" myth, are there theories as to the origins of these mythologies?

More submissions, of course, are always welcome, if anyone wishes to add something more.