The device known as shoyu-tai (or soy-sauce snapper in Japanese) was invented in 1954 by Teruo Watanabe, the founder of Osaka-based company Asahi Sogyo, according to a report from Japan’s Radio Kansai.
It was then common for glass and ceramic containers to be used but the advent of cheap industrial plastics allowed the creation of a small polyethylene container in the shape of a fish, officially named the “Lunch Charm”.
The invention quickly spread around Japan and eventually worldwide, and it is estimated that billions have been produced.
It could just be waxed paper/waxed cardboard like the milk cartons of yore, but small. A lot of this stuff has been around long before plastics, and we got by just fine :)