This is from the passenger list that Chempat found. It looks like Jerh was traveling with a Thomas Daig, based on the sharing of 1 box of belongings.
This could be "Duig" also, which could be "Doig" in the US or probably a variety of spellings.
If they were traveling together, there is a good chance they were neighbors in Ireland. What can you find out about Thomas?
There are probably a dozen people with his name out there but here is one of them:
Naturalized in Illinois Northern District, index only. but it would point you to his records.
https://www.familysearch.org/ark:/61903/1:1:XKL2-XWL Still it is a very early naturalization and probably won't tell you a lot.
Did Jeremiah Finn get naturalized? Was there an obit for him when he died? Did his children's records mention a better place of birth than just "Ireland"? Did any of his children die while he was alive, is there a record, and did the record ask for parents' place of birth? (I found someone's townland that way once.)
Figure out whether or not William Finn in Detroit is Jeremiah's brother or not and do the same for his records also.
Were there Duig families in the same locality as the potential father William Finn of Cork? Look for the Tithe Applotment books for Duig & variations in Cork, for example.
I don't know how common "Duig" is, I've seen it before but have never worked on any family of that name.