。
As evening drew near, it started to rain.
Literal
Evening-near rain [subject-が] fall-begin-[past-した].
夕方近く ('toward evening, around evening') is a compact time expression with the noun 近く ('vicinity, near') functioning adverbially. 降りだす ('to start raining') is a compound verb: the stem of 降る plus だす ('to start doing'). The compound ~だす pattern is productive: 走りだす (start running), 泣きだす (start crying).