November

He never closed his eyes, but kept them fixed on the Pleiads, on late-setting Boötes, and on the Bear - which men also call the Wain, and which turns round and round where it is, facing Orion, and alone never dipping into the stream of Okeanos - for Calypso had told him to keep this to his left.

So, Odysseus is navigating by the stars, the Pole star, the Bear or Big Dipper as it's more commonly known nowadays, Boötes and the Pleiades. The Pole star is always visible and Boötes most of the night, but the Pleiades make this interesting. Apparently, they were visible throughout the night at the time Odysseus sets off, which means this trip has to take place in late November when the Pleiades rise at sunset and set at dawn. The exact date of this phenomenon is November 22nd. This explains why Odysseus was so anxious, he feared the autumn winds! Finally, Athena's direction 'keeping the Bear to the left' is precisely what you need to do if you want to get to Scheria in a southern wind. So far all three locations fit Calypso's island.

and she sent forth a gentle wind and warm.

The emphasis on the wind being gentle and warm seems to suggest it was an otherwise cold period. Perhaps she sent a southern wind from North Africa? Anyhow, Odysseus finally sets off on the raft to Scheria.

Zoom

Pole star

Pleiades

Odysseus is helped on his way:

Odussey Book 5 line 251 Barry B Powell
Odyssey Book 5 line 404-407 Barry B Powell