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It can't possibly have rained during the night.
Literal
Night [gen-の] interval-during rain [subj-が] fell [impossible-はずがない].
~はずがない ('there's no way that X,' 'it can't be that X') is a strong epistemic denial — denies the possibility of a past event based on the speaker's reasoning. Contrasts with ~かもしれない ('maybe') and ~はずだ ('should, is expected'). Here the speaker has reasoning against rain.