Have you checked out this family? The son could have had a baby in 1934.

1930 United States Federal Census > Maine > Sagadahoc > West Bath > District 16

BROWN, Fred, 34, married age 21, b. ME, parents b. ME, machinist
Harriet, 34, married age 20, b. ME, parents b. CAN
Fred, Jr., 13, b. ME
Clara, 11, b. ME
Corrine, 9, b. ME
Winnifred, 7, b. ME
Richard, 5, b. ME

There is also a Fred P. Brown of Bath who married Eleanor Libby of Lewiston on 04-24-1933 listed in the Maine marriages online. Another Fred Brown of Bath (same one?) married Mary E. Pinkham on 03-17-1939.