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 don’t think that’s a hole. I think it’s the opposite, and an optical illusion.
https://en.wikipedia.org/wiki/Multistable_perception
Not true. "Shaft A
Baraize also paved with cement this deep hole (shaft A) on the top of the Sphinx’s head. The hole measures approximately 5 feet square and nearly 6 feet deep. An iron trap door was fitted to the mouth of the hole. It has been theorized that the hole, began as a means for affixing a headdress to the sphinx in the manner of the New Kingdom (see photo below), was later deepened in search of hidden chambers." From this site
And picture from 1925
Thanks!