Is there evidence that Isaiah 53 was viewed as a Messianic prophecy within Judaism, or is it an exclusively Christian interpretation?

The modern Jewish interpretation of the so-called suffering servant song of Isaiah 52:13-53:12 is that it is a prophecy referring to the nation of Israel, not the Messiah. As such, it is sometimes suggested that Christians invented the idea that this is a Messianic prophecy. What evidence is there that (at least some) Jews saw the passage as having Messianic implications? Do such interpretation predates the advent of Christianity? When did the nation of Israel interpretation become common?