The balance of the available evidence suggests that the family moved to the Albany Area soon after arrival in America.

Some sources state that Cornelis Cornelis  was a magistrate in Bedford, Brooklyn in 1673 which seems to be based on a reference to a 'Cornelis Jr. of Bedford' who held this office and who is mentioned in Teunis Bergen's 'Register of the Early Settlers of Kings County' (p 322). However, his name does not appear in O'Callaghan's Register of New Netherland or in any other source that lists the inhabitants of Bedford at this time.

Wilson Ledley, in both his 1959 and 1969 accounts of the van der Hoeven family, feels that this reference may relate to Cornelis [b Albany c1675], the son of Cornelis Cornelis van der Hoeven and Metje Beekman,  who did live in Bedford from 1690 onwards and held the office of Constable and Justice of the Peace there.  However, Ledley's tentative suggestion that the family may have been resident in Bedford has been taken up in several derived genealogies and gained undeserved credibility.

Early connections with Albany are : Adrientje, Geertje's sister and passenger on 'De Bever', married Jacob Joosten [van Covelens] at Albany in 1662. They had a child baptised at Kingston the following year. (Kingston Registers) Jacob Joosten had been Voorleser and Court messenger at Kingston since 1661 and was a colleague of Domine Gideon Schaets.

The principal contact with New Netherland was Dominie Gideon Schaets, who had been a schoolteacher in Beesd until his appointment as minister of the Albany Reformed Church in 1552. He would certainly have known Geertje van Vulpen, Huijgh Barents de Cleijn and other members of the group from Beesd during his time there and had possibly taught some of the older van der Hoeven children. Schaets is recorded as a member of the Beesd Reformed Church in 1644 at the same time that Geertje's uncle, Jan Dircksen van Vulpen, was a church Elder.
Geertje's eldest son, Gijsbert Cornelis, is mentioned in the Albany records as early as 1667 and was evidently well established as a woodworker and builder in Kinderhook by that time. The land in the Powel Patent of Kinderhook that Gijsbert bought in 1667 was still in the family in 1684. (Will of Geertje van Vulpen)
Elizabeth, daughter of Geertje, married Juriaen Calyer around 1667, by which time, Juriaen Calyer was residing and working in Kinderhook. (ESB 2:16 and various references in ERA, CMA) Their eldest son, Jochem was born at Kinderhook in 1668.
Two passengers on De Bever also from Beesd who settled in Albany were the young shoemakers, Hendrick Bries and Goosen Jansen Van Noort. Hendrick Bries was a witness to a power of attourney in August 1663 (ERA3:243) and accepted the son of Cornelis van Schelluyne as an apprentice in June 1664 (ERA3 287), indicating that Bries had been in Albany for some time. Goosen Van Noort bound himself to Willem Brouwer of Albany as a journeyman shoemaker in August 1661 (ERA 3:103) just a few weeks after arriving in America.
Geertje's marriage to Steven Jansen Coninck must have taken place before August 1673, when she is mentioned as his wife in the Albany Deacons' Accounts(ADA 246n)