The first evidence of true cold-brewed coffee, made with cold water, comes from Japan. Kyoto-style coffee, named for its popularity in Kyoto, Japan, is the earliest record of cold-brew coffee. It's clear that the Japanese were brewing coffee this way in the 1600s, although the record prior to that is unclear.
Think of a pour-over method but using cold water and taking much, much longer. The coffee is ground and placed in a chamber, above which sits a flask of iced water. The flask has a little tap at the bottom, which is set to allow the water to drip onto the grounds.