Birth Registration began in 1864, there are three Stephen Hogan’s on
https://civilrecords.irishgenealogy.ie One in Tipperary 1865 & two in Cork 1866.
So I guess as you say a little earlier.
The 1911 census states he was a widower but had been married for 17 years had 5 children 3 had died, this was crossed out as it was not required, it is normally in the wife's information.
Margaret was on the 1901 as born Liverpool about 1871, John 5 & Stephen 3 were both born Liverpool.
Stephen is not in Liverpool in 1891 but Margaret is, see below.
Ellen Bawsthome 50 Head Widow (As transcribed)
James Shepherd 26 Son-in-law Single
Margaret Shepherd 27 Daughter Single
No marriage record that I can see?
Colin