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.
https://www.smithsonianjourneys.org/blogs/blog/2020/05/20/photo-what-happened-to-the-sphinxs-nose/
It is possible it was destroyed by a Muslim for religious reasons though it is impossible to truly confirm.