Excellent question, Lorenza!
From what I know, ship passengers lists
were only recorded from 1890. Since Michael was a stowaway passenger, it might be difficult to find him this way either.
Another option would be to look for church records from county-based genealogy centers
, since Michael was born before 1864. Do you happen to know where in Ireland he originated?
You'll find more guidelines in our Ireland Family History section
and a complete overview of the resources you can use here
Best of luck and let us know how it goes!