I'm gonna say no, and here is why:
1. The outside shape is somewhat squarish, but not perfectly square. As you probably know, there are different indenter shapes for hardness testing, including round balls, square pyramids, and oblong pyramids. For this simple to have come from a hardness tester, the edges should be pretty sharply square.
2. I don't see any evidence of lines starting at each quarter and then converging on a single point in the middle of the square, as I would expect to see with an actual hardness indentation.
3. Generally speaking, a metrologist would take the hardness on as flat a surface as possible (such as the head of the drum head, rather than along the rim). It isn't a hard-and-fast rule, but rather just good laboratory practice.
4. There is only a single indention. Very often, multiple indents will be taken on the same object in order to get a better statistical sample size. Below I have posted a picture showing a line of indentions on a gear moving from the hardened outer surface inwards (the size of the indention is inversely proportional to the hardness).
Again, absolutely anything is possible, so I can't rule it out your initial theory completely. However, I'd much sooner believe that at some time in the last 50+ years, some random sharply-pointed object hit your quarter at that location. This scenario just seems much more likely to me.

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https://www.paulo.com/understanding...case-depth/)