DNA won't tell you nothing unless a whole lot of Gross's do it. I too am a Gross of Jewish descent. My family came from the Jewish community in Königheim, Baden beginning in 1852 and at least five of them came to Massachuetts - two of them, first cousins - were named Moses Gross! Ascher changed his name to Isaac in America, and Vietel called himself Philip in America - they did this sort of thing "to blend into the new life"!!! I would note there have been Gross's in Massachuetts from the mid-1600's, not necesarily of Jewish origin.
We received the Gross family name at the order of the Grand Duke of Baden (1809 Edict, 1811 Registration of surname). It may have been only a registration of an existing surname, it may have been a new surname, we can't tell; no one can tell.