The unicorn enters European writing as ethnography rather than fantasy, and it enters through one man.
Ctesias of Cnidus was a Greek physician who served at the Persian court in the late fifth and early fourth centuries BCE, and who wrote an account of India, the Indica, assembled from what he heard there rather than from travel. His description is specific: a wild ass, the size of a horse or larger, with a white body, a dark red head, blue eyes, and a single horn on the forehead about a cubit and a half in length, coloured white at the base, black in the middle and crimson at the tip. It is exceptionally fast and cannot be taken alive. Drinking vessels made from the horn protect against poison and convulsions. The flesh is too bitter to eat.
Every recognisable element of the later unicorn except the maiden is in that paragraph, including the horn as antidote, which is the detail that would eventually be worth more than its weight in gold.
Pliny the Elder repeats a version in the Natural History, describing a monoceros with the head of a stag, the feet of an elephant, the tail of a boar, and a single black horn two cubits long, which cannot be captured alive. Aelian and others follow.
What is being described is almost certainly a real animal or a conflation of several, the Indian rhinoceros is the usual candidate, and the horn-as-antidote belief attaches to rhinoceros horn in Asian pharmacology to this day. Ctesias was not inventing. He was reporting, at several removes, something that existed.