The first member of the Williams family who can be documented in North America is Jeremiah Williams. Much of the information about Jeremiah’s early life, however, is disputed. Some researchers maintain that he was born in England; other sources identify him as the Jeremiah Williams born in Wales in 1750 to William Williams and Ann Jones. The 1750 birth date does seem consistent with our Jeremiah’s age, as indicated by the ages of his children. However, no definite proof regarding his birthplace or his parentage has been discovered.
One reason for believing that Jeremiah might have been born in England or Wales is that immigration from those countries to Virginia is consistent with settlement patterns at the time Jeremiah and his family first appear in the records for what became Giles County. (At the time, it was still part of Montgomery County.) According to the book "Giles County, VA, History--Families," most of the early white settlers in that area came there from Pennsylvania, where their parents had landed as immigrants. These settlers traveled along an Indian trail known as the Great Wagon Road, settling on land along the New River.
The first record of Jeremiah’s existence is a grant issued in 1783, giving him 100 acres on the north side of Doe Creek as an assignee of Michael Drake. He later received grants of 35 and 60 acres in the same area. These land grants indicate that Jeremiah was prospering, as do the Montgomery County Personal Property Tax Lists for 1788 and 1789. According to these lists, Jeremiah owned six horses and no slaves. By 1791, Montgomery County Survey Book D recorded 46 acres “on the west side of land he now lives on” for Jeremiah.
In addition to acquiring land, Jeremiah was acquiring a large family. His marriage to Mary Garst took place before 1770, although a precise date has not been located. Several Williams family researchers have recounted the story of Mary’s birth: She was the daughter of German immigrants and was born during their voyage to America. It is said that her parents made a cradle for her from the oven of the ship’s stove. No documentation regarding the truth of the story, or who Mary’s parents were, has been discovered.
Mary and Jeremiah had twelve children—eight boys and four girls. The eldest son, Hugh, was born in 1770. Daughter Patience was born in 1772. Abram and David were born in 1775 and 1776, respectively. Molly was born in 1779, followed by John Stafford in 1780. Alexander was born in 1782, and Joseph was born in 1784. The exact year of Andrew’s birth is unknown, although he is believed to have been born between 1787 and 1789. James A. Williams was born in 1792; there is no record of what the “A” stood for. Margaret was born in 1794, followed by Rebecca in 1796.
 http://www.werelate.org/wiki/Person:Jeremiah_Williams_%2828%29
 http://www.wvgenweb.org/raleigh/BOOK/WilliamsJeremiahNyla.pdf