All we know about George Sr. is that his first child was born in 1893 and according to his kids' entries on the 1900 census, he was born in New Jersey.
So we can assume his DOB was before say 1875. I looked for a George Martin in Morris County in 1880, but there's only one--George E. Martin--and I don't think he's the same guy (unless he went on to marry someone else in 1900, which would be interesting).
That leaves us with just 58 guys named George Martin living in NJ in 1880. If it were me, I would research every one of them just in case, see whether they left the state or what happened.
How do you know his name was also George, by the way? Is that family lore or does his name appear on a death/marriage certificate of his children? I saw on Familysearch the New York marriage of George Jr. (as "George Brown" where he says his father was the second husband, and names his mother Sarah "Birt").
Records you could locate or order that would help
* birth cert of George (Martin) Brown, death cert
* birth cert of Mary (Martin) Brown, marriage cert, death cert
Also, the death cert of Sarah (Bird) (Martin) Brown would name her parents if known to the informant. Is the death and grave record I added to her profile the correct one?
There are a couple Morris County newspapers on newspapers.com and I see your grandmother's wedding announcement in there and also mentions of men named George Martin. Maybe he never left town.