Per Anderson in his Great Migration study, nothing known of William Adams who sailed on the Elizabeth and Ann at age 15. Origins are unknown, ancestors are unknown, and he is not known to have had any children.
Thanks to consideration of a document previously missed, Anderson has changed the narrative on this William Anderson. He is the same as William Adams of Ipswich, and now thought to be the son of William Adams who held land in Cambridge in 1635.
Still there is no evidence whatsoever as to his origins. His certificate to travel on the Elizabeth and Ann was signed in London.
William Adams of Ipswich is given in WikiTree here: His father is given a wife, and an ancestry from Shropshire - I don't think any of this is proven (if you follow Anderson). This profile needs sources which prove his origins and ancestry.