The early Emans/Emmons/Emmans family is traced fairly well in "An Emmons Genealogy" by Corwin Wilbur Emmons. Although it is out of print, many genealogy libraries have a copy.
Per this book, Geertje married Weynant (Janse) Bennet about 1740. He was the son of Jan Willemse Bennet and Alice Weynants Van Eyk. Weynant died before 1770. The book shows 3 children; Christopher, Weynant Joost, and Elizabeth.
This book shows Geertje (Geertie) as being the daughter of Jacobus Emans and his wife Geertje Romeyn, thier being married on May 10, 1700.
Jacobus is one of 8 children born to Jan (John) Emans. Jan's first wife was Sarah Jansen, and he later married Engeltie ____, but it is believed that all but the last child (Cornelia) were by Sarah. Jan is shown in a land grant in Gravesend, Long Island in 1645, but it is believed that he had been in North America for some time before that.
I hope this helps.
Scott