It might be safe to assume that Jan Pieterszen arrived in America between 1634-1662. One date frequently seen is 15 April 1660. At the time, the Dutch West India Company had an office in Hoorn.

According to the Haring Family Notebook, the marriage of Jan Pieterszen Harring and Grietje Cosyn on Whitsuntide (Monday, 26 May) 1662 was the "first recorded in the Peter Stuyvesant's Chapel" of the Nieu Amsterdam Reformed Dutch Church at Stuyvesant's Bowery, NY, beyond the wall of Nieu Amsterdam.

When Jan Pieterszen Haring & Grietie Cozyns were married in 1662, they settled on a farm located on Bowery Lane outside the wall of Nieu Amsterdam. From descriptions, this appears to be the 5 acres or immediately adjacent, granted in 1639 by the Dutch West India Company to Cozyn Garretsen, Greitje's father. It is described as " a house and garden on five acres bordered to the south by a certain swamp", likely the head-waters of the Minetta Creek (now Washington Square Park).

He became one of the Schepens to govern "The Outside People" beyond the wall on Manhattan Island. [By Dutch tradition, the office of Schepen was one passed down within families.] In 1681 Jan Pieterszen Haring headed a group that obtained a deed from the Tappan Indians of the Lenni Lenape Tribe for a large tract of land, and on 24 Mar 1686 the group obtained a patent from Gov. Dongan of New York (Tappan Patent of New York). Before he died in 1683, Jan Pieterszen Haring had purchased three shares in the names of himself and his eldest sons, Peter and Cosyn. While he never lived to settle on his new lands, his widow and several of his descendents (Cozyn, Cornelius, and Abraham) moved to the fertile Tappan region.

ref: Ferth Haring Fabend: A Dutch Family in the Middle Colonies, 1660-1800. (Rutgers Univ. Press, 1991). p 253.

Haring Family Notebook, copied (between 1824-1830) from the Haring Family Bible by Samuel Kip Haring

The Haring Family Notebook and the Origins of the Haring Family in Hoorn, Holland. Peter Haring Judd. NYGB Record. Vol 135 (3), Jul 2004. pp.169-174.

http://www.dutchdoorgenealogy.com/haring_notebook_1810.html