WHY DID the Jews believe someone was coming?
“I will raise up for them a prophet like you from among their brothers. And I will put my words in his mouth, and he shall speak to them all that I command him. And whoever will not listen to my words that he shall speak in my name, I myself will require it of him.” - Deuteronomy 18:18-19
This is a dual prophecy, one with a near fulfillment in Joshua leading the Israelites to the promised land, as well as a future fulfillment in Christ. Christ also leads people to the promised land, that is, the new Garden of Eden.
Also, Isaiah 51 is about the redemption under Christ and it says:
"The Lord will surely comfort Zion
and will look with compassion on all her ruins;
he will make her deserts like Eden,
her wastelands like the garden of the Lord.
Joy and gladness will be found in her,
thanksgiving and the sound of singing.
Listen to me, my people;
hear me, my nation:
Instruction will go out from me;
my justice will become a light to the nations.
My righteousness draws near speedily,
my salvation is on the way,
and my arm will bring justice to the nations."
This says that the world will be turned into a New Eden - I hope this is what you are looking for.