Index to Unassisted Inward Passenger Lists to Victoria 1852-1923
Index to Assisted British Immigration 1839-1871
Going on the age usually given for George, he was probably born in 1824, which means that if he arrived between 1851 and 1854, he would have been about 27 to 30 years old on arrival. The closest candidate by virtue of age would seem to be the 26 year old George Griffiths who arrived per the Hibernia in 1852. However, any of the ages recorded may have been incorrect, and the transcription for the index could have been incorrect, so they would all bear examination.
The Hibernia, it happens, came to Port Phillip from Liverpool, so that does increase the chances of it being the right George Griffith - but I don't know where the other vessels originated.
"List of vessels in Hobson's Bay, Sunday 10th October 1852": Hibernia from Liverpool.
LIST OF VESSELS IN HOBSON'S BAY. (1852, October 4). The Argus p. 6.
The other 26 year old George Griffiths who arrived by the Panama in 1852 is less likely as the ship appears (from advertising in The Argus) to have been engaged in a run from Australia to San Francisco and return.
I haven't discounted arrivals in other ports, but as I haven't thoroughly eliminated the Victorian arrivals, I'll leave those until later.