I’m not a native English speaker, but according to Wikipedia, new moon in English can also be a bit blurry.
The original meaning of the term ‘new moon’, which is still sometimes used in calendrical, non-astronomical contexts, is the first visible crescent.
Same for Japanese, on day 1 and 2 the moon is hard to see, but on day 3 we can see a thin crescent, that’s 三日月.