The date on the sign is 1602. That predates Plymouth Rock and Jamestown, and the other Martha’s Vineyard in Massachusetts.
From http://history.vineyard.net/hfnorton/history.htm :
“The next explorer, and the first one to leave any account of the island, was Bartholomew Gosnold, of Falmouth, England. In 1602 he sailed for Virginia. Contrary winds drove him to the Azores; thence he sailed a little north of west, and struck out boldly across the Atlantic. He was the first Englishman to sail directly to the American coast, thereby saving nearly a thousand miles in distance and at least a week in sailing time. He landed on a cape which he named Cape Cod from the abundance of codfish found there. Then doubling the cape and sailing to the southward he landed on a small island about six miles southeast of Gay Head. He called this small island Martha’s Vineyard. The next day he landed on the larger island. After exploring it and finding it so large, well wooded, and with such luxuriant grape vines, many beautiful lakes, and springs of the purest water, he transferred the name and called it Martha’s Vineyard, in honor of his mother whose name was Martha. The other island he named No-Man’s-Land.”