Coques was born in Antwerp as the son of Pieter Willemsen Cock and Anne Beys. There is no certainty regarding the exact date of his birth. Estimates range between c. 8 December 1614, the date on which a Gonzala Coques was baptized in the Antwerp Church of St. George (possibly an elder sister although female 'a' endings of first names of boys did occur in 17th century Antwerp) and 1618, the date under the engraved portrait in biographer Cornelis de Bie's book Het Gulden Cabinet of 1661. The later date is less likely since Coques commenced his apprenticeship in 1626 which would be a more likely date for a 12-year-old than an 8-year-old.