None of these people appear as witnesses to the baptisms of his children. Salomon Davids, the son of Joris Davidszen, did appear at the baptism of Andries' son David. It is also possible that he isn't related to any of them.
Possibly 7 Apr 1670 in Kingston?
Kingston notice of marriage banns Dec. 7 1701, #180 in Hoes, makes marriage likely late Dec. Renders name as Davidsen and says groom born Albany and resident in Kingston; bride born In Marbletown and resident in Kingston.
VanVliet Genealogy, LDS film 0940271
1701 Nov 22 Andries Davidse, y.m., b. at A., and Cornelia Van Vliet, y.d., b. at Mormeltown, both l. at King. Recd. cert. to be ma. at King. 
1701 Dec 07 Andries Davidsen, j.m., born in Albanie, and Cornelia van Vliet, j.d., born in Mormeltouwn, and both resid. here. Banns published, but dates not given. 
↑ Secretary Henry L. Bogert. "Albany Records, Marriages 1700 to 1725" in Year Book of the Holland Society of New York. New York: Knickerbocker Press, New York, 1905
↑ 2.02.1 Roswell Randall Hoes. Baptismal and Marriage Registers of the Old Dutch Church of Kingston, Ulster County, New York: (formerly Named Wiltwyck, and Often Familiarly Called Esopus or 'Sopus), for One Hundred and Fifty Years from Their Commencement in 1660. New York: De Vinne Press, 1891.
It may be possible to confirm family relationships with Andries by comparing test results with other
carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share DNA with Andries: