The answer to this question depends on the time period. Europeans have at least known about the exotic animals that you mention for a long time. Since the Greek and Roman cultures relied heavily on Mediterranean trade and had colonies in Africa and Asia, they were exposed to these animals early on. However, obviously not all Greeks/Romans were actually traveling themselves, and often even though they had heard a description of the animal, they'd never seen one. This made importing these animals very popular, as it was a way for rich/powerful people to show off by supplying animals for the arena or using them as living status symbols, and for poorer people or people who couldn't travel (eg women) to see the animals for themselves. Julius Caesar famously imported the first Cameleopard (ie giraffe) for reasons along these lines.

Later, the Roman knowledge of these exotic animals was transferred to other areas of Europe touched by Christianity. Animals like elephants or the cameleopard, or the phoenix, or the unicorn, were all considered to be in existence somewhere in the world, just beyond the reaches of Medieval Europe. In Bestiaries, which are books which list animals and describe them in terms of both zoological and religious significance, all of these animals, as well as commonly encountered ones such as the ant or the dog, would be described on equal footing. Bestiaries were often illustrated, and some of the depictions of animals we know to exist were quite fantastical. Some of these exotic animals were brought into northern Europe, for example Charlemagne was given an elephant, but these encounters were rare, and these animals existed in the imagination only for most people.

Later, during the Early Modern period, Europeans began encountering these animals again, and importing them more frequently and in larger numbers into places like England and France. At this point they started teasing out the concept of the mythical creature (cameleopard, real, but not exactly as described, unicorn, not real) and applying the new ideas developing in natural philosophy to them, rather than being foremost interested in their religious symbolism.

Eventually, exotic animals were sought after in a systematic way by naturalists like Darwin who wanted to fit them into new frameworks like Linnaeus's taxonomies and Darwin's eventual evolution.

And now scientists look for new species, and we react like this.