Actually, I myself didn't know. I always figured it referenced a mold for industrial reproduction, but your explanation does make sense. Either metaphor would work, actually, for the implication intended.
The die is cast
What does the saying "the die is cast" mean?
idiom. used to say that
a process or course of action has been started and that it cannot be stopped or changed. Once we signed the contract, the die was cast, and there was no turning back.
The etymology is not discussed.
A die is a specialized machine tool used in manufacturing industries to cut and/or form material to a desired shape or profile.
It seems either origin is possible.