We must assume that the answer is yes regarding ancient belief, although the subject of belief can be soft - difficult to evaluate and understand with contemporaries and terribly difficult, therefore to address in past times. Since folklorists documented living traditions complete with what appeared to be active belief in magic and elves - etc. - until relatively recent times, there is no reason not to project that sort of point of view into earlier times.

The following are some paragraphs I wrote for similar recent questions (I include, here, dragons under the part of your question that asks about "other species"):

Dragons were generally believed to have existed, but the folk typically relegated them to distant times or places. There are no legends of people coming upon them in the wild. Even the celebrated observation in the Anglo-Saxon Chronicle of dragons being seen in the clouds is a literary report that was likely something the chronicler heard - a legend from a distant place. Whether we can regard that as an exception or not, folklorists working with pre-modern informants did not collect western/northern European legends about encounters with dragons. People did believe the once existed, and these entities do figure in folktales, because these fictional stories were often set in remote places and times. Giants fit into folklore in much the same as dragons.

Fairies (and all their kindred with the multitude of names including pixies, elves, hidden folk, etc.) were a matter of belief, and pre-modern informants of western/northern Europe were consistently recorded telling legends about encounters - stories that were told to be believed. People felt that encountering the fairies was a very real possibility, and they regarded this possibility as terrifying because the powerful entities usually interacted with people with ill effect. The worse case scenario was abduction and this meant that there would be an eternity of servitude with no possibility for heavenly salvation. Less horrible outcomes could mean everything from poor luck to being maimed, blinded or otherwise burdened by some ill effect.

One should take the idea of belief too far, however. There have always been skeptics, and there is good evidence that people also believed that previous generations believed more than they do "today" - whenever "today" was. So the belief was not spread around consistently, and any one person might believe more one moment than the next. Nor should we regard belief in fairies (using the variety of names) as extinguished: belief survives in parts of Britain and Ireland as well as Iceland and Scandinavia.

By modern analogy, we can consider belief in ghosts - or even angels. These entities are not universally recognized as real, but many people believe, and many people might be more prone to believe in ghosts, for example, when crossing through a cemetery at night! Circumstance is everything. These entities are part of modern culture for many people, and so people can draw on them when they feel the inspiration.

And here are some more similar thoughts, but these specifically dealing with the question of "who came up with the idea" of these types of entities. To this, the simple answer is that the origin is embedded in a distant, unknowable past, but we must also concede that there was likely never a single point of origin where a single person came up with these ideas. Instead, cultural legacies were passed down and transformed, inheritances with roots that likely reach back tens of millennia. Again - a few paragraphs:

The idea that there is "an element of truth behind every folk legend" - and by implication behind each of these creatures - is in itself an element of folklore that is not usually verifiable in reality. This line of thinking is referred to as Euhemerism, taking its name from the 4th century BCE Greek writer, Euhemerus. He asserted that the stories and beliefs in the gods grew out folk recollections of real people. By implication, we can search for "real" things that inspired other entities in folklore.

This idea is generally discounted by trained folklorists even while it is frequently embraced on the internet - and by many questions on /r/AskHistorians. One often finds explanations: elves and fairies are folk recollections of early, presumably short indigenous populations; trolls are recollections of Neanderthals; dragons were inspired by dinosaur bones or by a primal fear of snakes (so which one is it?); the cyclopes was inspired by an elephant skull; mermaids were inspired be seals of manatees.

These explanations are pure speculation, and there is no evidence that folk belief in the supernatural follows a path from the real to the extraordinary. Could these "real world" things contribute to belief? Perhaps, but that suggestion is also speculative, and proof to back up this idea remains elusive.

We must concede that folklore is a broad river with many tributaries. It is possible that something from the real world could serve to reinforce and give strength to a belief, but just as it is not possible to determine the source of water downstream - which tributary is the source of the water in this bucket? - it is not possible to sort out how real-world factors may have contributed to folklore at one time of another.

It would be a tidy package to ascribe various supernatural beings to this or that cause, but unfortunately, folk belief and tradition doesn't work that way, and I would defy anyone to prove the opposite. Speculation is fun, but that is all it is.