If William emmigrated from Liverpool when he was 3 years old he will have travelled with his family and become an orphan after his arrival. Your first attack must therefore be via the passenger list for the Australia docking in NY on 3/10/1853.
This is available online but there is a cost. You can find it by going to www.cyndislist.com/ships. This should give you the complete family including his parents and siblings at that date. Look out for siblings born after that date in USA.
Whilst searching I found a William Press aged 1 at the time of the 1851 UK census. His birthplace was given as Stafford, Staffordshire, England. You would need to see all the houshold names in this census to see if they matched the passenger list. Again it's pay to view.
You may also be interested in the 1920 US census which lists a William M Press, born 1850, England, living with his spouse Mallie Press, in Collin, Texas.
Did Sarah Jean die and did he re-marry later in life?
Good luck with your research