I’m second generation American. My fathers side of the family is from the Ukraine,
Are you sure ? Part of Ukraine and part of Poland... at one time were Galicia.
This is important, if you try to trace his roots. It is reasonable to assume that anyone from Galicia might have been Jewish. Not always the case though.
Ancestry.com has records for your spelling/name
It's possible that the original name had a slightly different spelling. I found a few close matches.
Check: Ellis Island Records.... for family who entered the US
Search for Naturalization Papers
If any member of the family served in the US military... check military records.
Check old papers and documents for clues. It's possible that an old aunt has something in the back of a drawer. You never know.
Place names are very important.
Speak to other family members for information.
Look at old photos... for military uniforms... specific buildings... etc
We can help with photos and text, if needs be.
There are some good links in the Genealogy Resources. It just takes time to find the right one.