Thanks for your kind assistance, Pauline! The census and immigration records you found do indeed refer to my great grandfather, Mathias Haas (rather than another person of the same name). While greatly appreciated, they are records that I had previously.
As my intent is to confirm the earlier lineage, I do wish to respond to your question regarding siblings. I found online records for a sister Gottlieb (b: 1851, d: 1853) and an unnamed "Baby" Haas (d: July 26 1854).