After twelve miserable and lonely years living with her Aunt Gormlaith, Isolt escapes, taking with her Gormlaith’s wand (originally Salazar Slytherin’s) and a brooch shaped shaped like a Gordian Knot, which had belonged to Isolt’s mother. Isolt first goes to England, but Gormlaith is able to track her there. Isolt then cuts her hair and boards the Mayflower, in disguise as a Muggle boy named Elias Story. Once on land again, Isolt leaves the Puritans behind her and goes to live in the mountains (Pm).
It is uncertain how long this event took or when it began, exactly. But we know that Isolt was born around 1603 and fled Hag's Glen at eighteen (because she was five when she went to live with Gormlaith and it was another twelve years before she escaped), so it should be about 1620. It must have been the earlier part of 1620 or perhaps 1619 because canon says the Mayflower arrived in late 1620 and Isolt would have had to make her way to England and then sailed all the way across the Atlantic in a seventeenth century ship. In real history, the Mayflower departs July 1620. It arrived at Cape Cod in November 1620. Canon implies the Mayflower lands in winter, but November is essentially winter in New England, so this isn't necessarily a discrepancy (source: Wikipedia).
A boy or young man named Elias Story really is recorded as a passenger on the Mayflower (source: Wikipedia).