The idea with cesium-137 is that it didn't exist naturally in significant quantities prior to 1945. An airtight container, sealed from the atmosphere prior to 1945, should not contain any.

It's not like some other radioisotopes using in dating, such as carbon-14, which are continuously produced naturally (i.e. by cosmic rays initiating nuclear reactions in the high atmosphere). In that case, an airtight container had a known concentration at the time of its sequestration, and radioisotope dating (to oversimplify) counts the number of half-lives that elapsed since that point. (Or with the example of organic matter—the number of half-lives since a tree was felled into lumber—since it ceased metabolizing atmospheric gases).

Half life is just time until only half of the original amount remains. Double that and it represents the time it takes to halve again. The actual detection threshold would be separate from half life.

Wouldn't that just mean that the detector needs to be increasingly sensitive to detect a late-1940's forgery?