The Mishnah, the rabbinic guide to matters of halakha (legal regulations and requirement to do with the Law of Moses), contains a tractate describing the high priest's preparations for the Day of Atonement, when he would offer up a sin-offering on behalf of all Israel.
It closes with a reminder, attributed to r. Akiva, of who it is who actually makes Israel clean.
How fortunate you are, O Israel! Before whom are you made clean? Who is it that makes you clean? Your Father that is in heaven! As it is said (Ezek 36:25) "And I will pour clean water upon you, and ye shall be clean"; it says also (Jer 17:13), "the mikveh of Israel is the Lord"- even as a mikveh makes clean those who are unclean, so the Holy One, blessed be He, makes Israel clean.
Mishnah, t. Yoma, 8:7.
The word in bold is usually translated in English as hope, but it was seen as an allusion to the practice of ritual bathing, which was done in what was termed a mikveh. The association is further strengthened by the rest of the verse, which calls the Lord the fountain of living waters. Living water was the essential component in the mikveh, without it one could not become clean.
I'm not too sure that the wordplay isn't Jeremiah's, he certainly picked an unusual form of the word hope.
Whilst actions were paramount in Judaism, the sages recognised that it was God who made them efficacious. In that respect, there was not that big a difference between them and the early Christians.