Dear Ms. Clarke,
Thank you for posting your request on History Hub!
Because you are seeking information about ancestors before the colonies were firmly established in North America, you will need to search for genealogical information or relevant materials from their country of origin such as The National Archives of the United Kingdom.
Prior to 1789, there was not an entity creating or maintaining passenger arrival lists at the Federal government level until the U.S. Customs Bureau started overseeing ports. One index source that you should use is P. William Filby’s “Passenger and Immigration Lists Index, 1500s-1900s” (15 vols) that is searchable through Ancestry.com. Another online source available is a collection of lists Olive Tree Genealogy has gathered.
We hope this is helpful. Best of luck with your family research!
[Information provided by Elizabeth Burnes, Subject Matter Expert]