I suspect that this is the WHH you are seeking, on the LDS Family Search site-
William H. Hawley United States Census, 1880 birth: 1833 England residence: 1880 Boston,? Suffolk,? Massachusetts,? United States spouse: Mary T. Hawley children: Nellie Hawley,? Thomas Hawley...
It looks as though you have found this Naturalization Entry on the LDS FS site-
name: William H Hawley event: Naturalization event date: 1867 event place: Massachusetts age: birth year: 1832 birthplace: Great Britain nara publication title: Index to New England Naturalization Petitions, 1791-1906 nara publication number: M1299 nara roll number: 75 film number: 1429745 digital folder number: 4639191 image number: 07086
You should treat that date with caution; and also as typewriters were not invented until much later than 1867, there could be transcription errors from the original manuscript document to that card.
Statutory Registration of Births did not start in England until July 1837,m so we are dependent on Parish Registers for earlier years; and the surviving PRs have not all been computerised etc.
FMP does not have any Baptismal/Birth Records for a William Hawley around 1832,
Checking in the period, 1822 to 1842, the earliest is 1838.