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I looked all over for a date and got everything from "early 1800s" to "late 1800s" but nothing exact, so I had to make an educated guess. The first cameras practical enough to take such a photo were developed around 1840 and the excavations began in 1867.
I too was trying to find the date of this photo this week. To narrow your time span, the first aerial photograph (also from a balloon) was taken in 1858 in France. So this photo had to have been taken after that point.