Jeremiah's own identical date formula for the siege's beginning - Ezekiel, far away in Babylon, records the same day the historical account independently confirms.
Again, in the ninth year, in the tenth month, in the tenth day of the month, Yahweh’s word came to me, saying,
In the ninth year of his reign, in the tenth month, in the tenth day of the month, Nebuchadnezzar king of Babylon came, he and all his army, against Jerusalem, and encamped against it; and they built forts against it round about.
This closes the entire ch.12-24 judgment-on-Israel section on the exact day the siege actually began, anchoring years of allegory and warning to one dated, historical moment.