I think this is really something that different kids will know at different times - because it's a symbol, not a kanji character, as the linked question answers.
I personally was taught this symbol and its origins by asking my teacher when I was in the middle grades of elementary school, but that's just me. I'm sure that there are others who knew about it earlier, and others who never learned about it from their teachers.
In fact, I remember that in my Japanese textbook, this symbol suddenly appeared in the text and there was no explanation of its meaning or origins.
However, when it appeared in the Japanese textbook, everyone probably already knew the meaning of the symbol somehow, and since the word itself is very common(like 時々, 人々, 堂々, etc...) , I guess no one asked about it.