Bauman Immigrants Mid 1800s

I am very much in need of help, I've hit a brick wall. My great great grandfather, Frederick Bauman came over from Germany when he was a child.One census lists that he arrived in 1845 when he was 6 another census lists 1852 as the year and he was 13.From his marriage certificate (St. Joseph's Catholic Church in Roch.It was a german parish) his father is listed as Mich. (Michael) and his mother is given as Margaretha Volz.On his death cert his father's first name is given as Midi (a nickname?).I can find no records on his parents and none on him prior to the 1868 Rochester Directory.It is like he just magically appeared in Rochester one day.Does anyone have any further info on his parents or his whereabouts prior to 1868 or where in Germany they may have been from?Any help would be appreciated!!