Photo of the Sphinx taken from a balloon before it was excavated. I can't find a date, but based on when it was excavated and the history of photography, some time between 1840 and 1867
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.
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