He appeared two years ago out of the blue and became popular in the blink of an eye.
"out of the blue" は「どこもないから急に現れる」といった「藪から棒に」のことのよく使われる慣用語です。
そして he appeared out of the blue と言います。
「瞬く間に」の直訳のような英訳があります: in the blink of an eye
その人は became popular のは in the blink of an eye で、合体すると
He appeared two years ago out of the blue and became popular in the blink of an eye.