We know from records in Billerica and Woburn that:
"Jonathan Baken and Elizabeth Giles of Billerica were marryed Jan 3d, 1694."
We know from Billerica records that Jonathan and Elizabeth, both named, had seven children there 1695-1709.
We know from Bedford records that "Mrs. Elizabeth Bacon the wife of Jonathan Bacon died the 16th day of December 1738," and from her grave marker that she was in the "67th year of her age," so born about 1671.
The author of Bacon Genealogy (1915, p. 34) asserts that this Elizabeth Giles was "daughter of John and Elizabeth [sic] Giles of Beverly." Unfortunately he doesn't provide any evidence or argument for this claim.
The author of Giles Memorial (1864, p. 160) states that he doesn't know where she came from: "Who was the father of Elizabeth Giles of Billerica, who was m. to Jonathan Baker [sic] of Woburn, Jan. 3, 1694-5?" The way the marriage is recorded does seem to suggest that both Jonathan and Elizabeth were "of Billerica" (other records on the same pages specify the bride's and groom's residences separately when they differ). But a full-text search of Giles Memorial fails to turn up any Giles families in Billerica at that time or indeed any other time.
Giles Memorial's profile for John Giles of Salem and Beverly (pp. 11-13) names only five children, Elizabeth not among them. However, records for John Giles' family are sparse, practically nonexistent prior to 1679. Only three of the five children's births are recorded, and he didn't leave a will. There'd be room for Elizabeth in the family, as John's first wife gave consent to a deed in 1671, indicating he was married by then. (We don't know her name, only the deed and that John was a widower when he married Elizabeth Wyman in 1679.)
John's older brother Eleazar Giles and his wife Sarah More of Salem Village had a daughter Elizabeth, b. 7 Dec 1667; Giles Memorial has no further record of her, and she isn't profiled on WikiTree.
Of interest is the fact that John Giles named a daughter Bridget, after his mother, in 1683; this daughter died young in 1689. Jonathan and Elizabeth (Giles) Bacon named a daughter Bridget in 1707; she died unmarried in 1731. This is the only occurrence of the name Bridget anywhere in Bacon Genealogy, suggesting it came from her mother's side.
It seems to me either one of the Giles brothers could possibly be Elizabeth's father: I think the strongest argument in favor is the naming of Bridget Bacon (which slightly favors John, who also had a daughter Bridget, over Eleazar, who didn't), while the strongest argument against is that neither family was anywhere near Billerica. Either way, there's just no evidence.
I'd be inclined to disconnect all parents from Elizabeth (Giles) Bacon and link to John and Eleazar as possible fathers in a Research Note. Thoughts? Any primary source evidence I'm missing?