Abel proposed that fossil skulls of Pleistocene dwarf elephants, commonly found in coastal caves of Italy and Greece, may have given rise to the Polyphemus story. Abel suggested that the large, central nasal cavity (for the trunk) in the skull might have been interpreted as a large single eye-socket.Cyclopia, a rare birth defect, can result in foetuses which have a single eye. Although the possibility has been raised of a link between this deformity and the myth of the one-eyed Cyclopes, in such cases, the eye is below the nose—rather than above as in ancient Greek depictions.As noted above, Walter Burkert sees the possibility of the Hesiodic Cyclopes having ancient smith guilds as their basis. See also
Polyphemus § Possible origins, for stories of other cyclopian giants similar to the story of Polyphemus encounter with Odysseus
List of one-eyed creatures in mythology and fiction

Notes
References
Apollodorus, Apollodorus, The Library, with an English Translation by Sir James George Frazer, F.B.A., F.R.S. in 2 Volumes. Cambridge, Massachusetts, Harvard University Press; London, William Heinemann Ltd. 1921. Online version at the Perseus Digital Library. Bakker, Egbert J., The Meaning of Meat and the Structure of the Odyssey,  Cambridge University Press, 2013. ISBN 978-0-521-11120-1. Bremmer, J.N. (1987). Odysseus versus the Cyclops, in Myth and Symbol. The Norwegian Institute. Burkert, Walter (1982). Structure and History in Greek Mythology and Ritual. University of California Press. ISBN 978-0-520-04770-9. Burkert, Walter (1991). Greek Religion. Wiley-Blackwell. ISBN 978-0-631-15624-6. Caldwell, Richard, Hesiods Theogony, Focus Publishing/R. Pullins Company (1987). ISBN 978-0-941051-00-2.
They have no agriculture, no wine, and live on milk, cheese and the meat of sheep. They live solitary lives, and have no government. They are inhospitable to strangers, slaughtering and eating all who come to their land. While Homer does not say if the other Cyclopes are like Polyphemus in their appearance and parentage, Euripides makes it explicit, calling the Cyclopes "Poseidons one-eyed sons". And while Homer is vague as to their location, Euripides locates the land of the Cyclopes on the island of Sicily near Mount Etna.Like Euripides, Virgil has the Cyclopes of Polyphemus live on Sicily near Etna. For Virgil apparently, these Homeric Cyclopes are members of the same race of Cyclopes as Hesiods Brontes and Steropes, who live nearby. Cyclopean wall-builders
Cyclopes were also said to have been the builders of the so-called Cyclopean walls of Mycenae, Tiryns, and Argos. Although they can be seen as being distinct, the Cyclopean wall-builders share several features with the Hesiodic Cyclopes: both groups are craftsmen of supernatural skill, possessing enormous strength, who lived in primordial times. These builder Cyclopes were apparently used to explain the construction of the stupendous walls at Mycenae and Tiryns, composed of massive stones that seemed too large and heavy to have been moved by ordinary men.These master builders were famous in antiquity from at least the fifth century BC onwards. The poet Pindar has Heracles driving the cattle of Geryon through the "Cyclopean portal" of the Tirynian king Eurystheus.