All we know for sure is that the image was made on the Illinois prairie, in the 1700's (18th century).
Since Brady was born in the 1820's, it seems unlikely that he did it, despite his pioneering (yet largely unpublicized) work in digital photography, and acknowledging that the fact that time travel hasn't been perfected YET doesn't preclude the possibility). An alternate hypothesis: the image was created in the 1700's by someone using Vermeer's secret camera obscura technique from the late 1600's.