I speculate that William came to the Virginia colony in the late 1600s but there is no way to document this since many of those records were lost during the Civil War. It would make even more sense if he arrived sometime after his father's death in 1682 since he would not have had immediate family ties to bind him to England. Tyrell Dalton was a justice of the peace in Cambridgeshire and was important enough to have been interned in the local church. Therefore, I guess that William had some means to support his venture to America. FYI, below is a picture of the tomb (and inscription in Latin) for Tyrell Dalton.
*Note--This lineage will need further research to confirm.