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.
As the article is lacking some information, here is a translstion of a part of the German Wikipedia article:
TLDR: As the Great Sphinx still has had its nose around 1200 A.D. and was already noseless in 1738, its nose must have been destroyed in the meantime, supposedly by some furious sheikh in 1378.