There are several born about the right period and in the right area
Burke, George William 1868 March Manchester (1837-1924) Lancashire 8d 219
Burke, George William 1870 September Salford Greater Manchester Lancashire 8d 65
BURKE, George William 1871 March Manchester (1837-1924) Lancashire 8d 246
Burke, George William 1873 June Oldham Greater Manchester Lancashire 8d 625
Burke, George William 1875 December Manchester (1837-1924) Lancashire 8d 191
I would normally think of only the first and the third one as he was born in January [or was he?] but the years are wrong except perhaps the 5th and it was not too normal for a January birth to be registered in December.
He was consistent about his year of birth on the censuses. I have found that people who lie have difficulty in remembering the lie whereas the truth is always easy to remember. For that reason I would focus on 1878. The next question is what were his birth certificate names? They might not have been G.W. in that order or without another before them.
Lastly, what do the Ellis Island records say - and the shipping lists?