From the most ancient rabbinic writings this passage was interpreted to be messianic. On rare occasions some rabbis interpreted the Servant to speak of King Hezekiah but that was extremely rare.
What the rabbis could not reconcile are the contradictory messianic prophecies of a suffering, dying Messiah as over against a conquering, reigning, and royal Messiah. Will He come riding upon a donkey or riding upon a cloud? A minority of rabbis chose an either/or option: if Israel is righteous, He will come riding on cloud; if Israel is unrighteous, He will come riding on donkey. The majority of rabbis were uncomfortable with that option and innovated a two Messiah view. The first Messiah will be the Messiah Son of Joseph or Son of Ephraim who will fulfill the suffering and dying prophecies. He will be killed in the Gog and Magog war. Then will come the second Messiah, Messiah the Son of David, who will win the Gog and Magog war, resurrect the first Messiah back to life and bring in the Messianic Kingdom and Israel's final restoration.
However, around A.D. 950 a new interpretation was inaugurated ...