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.
Archaeologists still do lots of digging, and sometimes even leave what’s dug up there, although it’s often reburied. And it is true that archaeology is inherently destructive. But it’s sometimes also necessary to learn anything about the past. Also, in the case of the Maya, it’s often more about clearing away vegetation than it is digging things up. The vegetation is already being destructive, so clearing it is often the best thing to do.