I would say it depends on what you mean by "sunglasses". To my knowledge, the first sun shades that were designed to be worn over and protect the eyes from overt sunlight (both direct and reflective sunlight) were "snow goggles" first employed by early Eskimo peoples (such as Inuit and Yupik) who typically lived in the northern circumpolar regions of our planet, primarily in areas like today's Siberia, Alaska and Northern Canada.
The use of these "snow goggles" is [said to go back at least 2000 years to the "Old Bering Sea" culture, who lived primarily around the Alaskan area near the Bering Sea/Strait](http://www.canadacool.com/location/worlds-oldest-sunglasses/) as early as 400BC. This cultural group are considered the ancestors of the more modern "Inuit" groups.
The purpose to these "snow goggles" was to protect the eyes from "Photokeratitis" - a blindness condition that in this case was caused by a combination of direct sunlight and reflective UV sunlight rays bouncing off the very bright and highly reflective snow surface. These goggles were worn over the eyes and had small horizontal slits in them to dramatically limit the amount of UV light that the eyeballs/pupils were directly exposed to. They were typically fashioned from caribou antler or different types of wood, and were held on by a strap around the head typically made of some type of animal sinew.