The ancestry of Archibald Stark (1693-1758) has not been satisfactorily identified. According to Wikipedia, he was born in Glasgow, Scotland, to parents who were from Wiltshire in England. It would appear that nothing more is known about his ancestry.
Wikipedia: John Stark
https://en.wikipedia.org/wiki/John_Stark#cite_note-3
According to the late Howard Parker Moore: "It seems that the parents of Archibald may remain conjectural. The New Hampshire Starks transmit no information. Not even traditions speak of John Stark's grandfather and grandmother."
A Life of General John Stark: 20
https://archive.org/details/lifeofgeneraljoh00moor/page/20/mode/1up
The absence of accurate information about Archibald Stark's ancestry is reflected in James R. Clark's discussion paper which was reproduced by the Stark Family Y-DNA Project
Stark Family Y-DNA Project
https://freepages.rootsweb.com/~clovis/genealogy/y-dnag2willofdullu...
In view of the absence of reliable information for the ancestry of Archibald Stark I believe that he should be disconnected from the family tree of John Stark and Susannah Archibald. Contrary opinions supported by evidence would be welcomed.