Peter Bieger immigrated to the States about 1847, probably settling in Cincinnati, Ohio. He married there in 1849 and by late 1850, he was in Illinois, where he purchased a small home/tavern.
The best place to search for his Germanic origins: Illinois. Peter left only two records in Ohio, none of which name any witnesses or associates. His 1856 estate settlement and guardianship for his children has the names of several witnesses and associates, most of which appear to be Germanic in origin. Searching these associates may provide some clue to his origins--and should be done before continued work in the larger Cincinnati area where the number of Germans is much larger.
Sometimes the best approach to immigrants is to completely research them in the area of settlement.