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I don’t think it’s intended to be played without that tip. It is technically possible to miss, but you’re very likely to learn about that before the game even tells you how to save…
(Mind you, I’ve only played the N64 version. They might have changed things in a re-release.)
Majora's Mask (how that tip is usually learned)
The game offers to tell you about that any time you talk to the scarecrow, which people usually do on the way to the observatory for the first time.
The trickier bit is that they tell you about it before you’re capable of using songs, so you have to remember that you can actually use it once it’s possible to do.