When the thunder rumbled, it started to rain.

Literal

Thunder [subject-が] sound-[when-と], rain [subject-が] fall-began.

The と conditional here is the temporal/sequential 'when X, then Y' use — essentially 'no sooner X than Y.' 鳴る ('to make sound / ring') is intransitive, contrasted with 鳴らす ('to make [something] sound,' transitive) — same pair as. 降り始める is a compound: 降る ('fall/rain') + 始める ('begin') = 'begin to fall.'