Diane, you're lucky to have such a small area to search through. The good news is that it was almost completely uninhabited in 1853. He was probably born in one of the lumber camps just set up in that part of the state, as few families had settled in the Saginaw valley just yet.
However, you've been given a little misinformation. Back then, this area was part of the very large "Hampton Township" of Saginaw County. It was another few years before Bay County was formed out of Saginaw Co, and it extended most of the way up the Bay. Arenac later broke away from Bay Co. But to the best of my knowledge, Worth/Standish/Pinconning/Gibson were never part of Midland Co.
The best reference for you is probably the 1854 Michigan census, which is on film and available either through the LDS or by interlibrary loan through the Library of Michigan.
The only "permanent" residents of Worth at that time would have been the Ojibwa tribe. Everyone else moved as the lumber mills moved. Some of the better books you might invest in are by Prof. Jeremy Kilar: "Bay City Logbook: An Illustrated History", "Saginaw's Changeable Past: An Illustrated History", and "Michigan's Lumbertowns: Lumbermen and Laborers in Saginaw, Bay City, and Muskegon, 1870-1905".
As for birth records, there really aren't many. If you can find a baptismal record (probably from one of the early churches in Bay City), count yourself very lucky. The majority of the time, babies were born and grew up before anyone even counted them as people. In the more remote parts of the state (and this would have been one of them), there weren't even regular churches. A priest or minister might come past every few months to handle any needs at the camp, but the rest of the time they were on their own.