I guess you could say it was a lucky break — I got a job through an acquaintance's introduction.

Literal

Gourd-from horse [quotative-って] say [wonder-のかな] acquaintance [possessive-の] introduction [by-で] job-placement decided [casual-ちゃったんだよ].

瓢箪から駒 is an idiom meaning 'an unexpected good outcome from an unlikely source' — literally 'a horse from a gourd.' って言うのかな softens the claim. 知人の紹介で is 'through an acquaintance's introduction.' 決まっちゃったんだよ uses ちゃう (casual てしまう) with the explanatory んだ, conveying pleasant surprise.