Laurette, Have you thought of reviewing your assumption that you have the correct GRO birth certificate from 1846 - his age at marriage, and at death, give’s William’s year of birth at about 1852.
It is possible the ROBERTS (William’s second name) is the surname of his father, and that he was an illegitimate birth.
His mother may have married later to HILL, and so surnames were changed. William may not have arrived in Australia with the surname Hill.
HILL , GREEN and ROBERTS are all are rather common names to work with unfortunately.
There are a couple of births where no mother’s name is recorded that might be possible avenues of investigation:
ROBERTS, WILLIAM -
GRO Reference: 1851 D Quarter in LIVERPOOL Volume 20 Page 269
ROBERTS, WILLIAM -
GRO Reference: 1849 J Quarter in LIVERPOOL Volume 20 Page 379