Germany is a pretty big place, and if you do not have further information to narrow it down, you will have a hard time finding anything. Church records for many communities are available online at ancestry.com (as you noted), but if a search there does not find anything useful, then you are probably out of luck. :(
I had a look at the landing record of 1884. There is a bit more information:
Friedr. Matz, age 34, farmer, from Prussia, traveled with
Ottilie Matz, age 26 years (his wife)
Hulda Matz, age 3 years (his daughter)
Otto(?) Matz, an eleven-month old baby boy.
This allows a couple of inferences:
1. Friedrich Matz was born around 1850 (plus or minus nor more than a year. If you are lucky, this will give you a birth record and a community.
2. He married his wife Ottilie (born approx.1858) not much before 1880 and not much later than that, either. Knowing the community might give you a marriage record with Ottilie's LNAB, and then you may be able to bootstrap birth records for the other members of the family, Ottilie's parents, etc. It's not going to be easy, but I think there is hope.