One of the common misconceptions about Jesus is that He never claimed to be God, and that the Jews never believed the Messiah would be “God”. The reality is neither of those assumptions are true.
The part about Jesus claiming to be God is easy to demonstrate from the Scripture, since Jesus took the name of God for Himself, made Himself “equal with God” in the eyes of the Jews, accepted worship as only God was allowed, and forgave sins as only God could. In the eyes of the people around Him, Jesus clearly made Himself out to be God, and they specifically tried to kill Him for it a few times.
However, I’ve always believed (because I heard a rabbi say this once) that the Jews never looked for the Messiah to be Divine.
Turns out that isn’t exactly accurate either. The Essenes were expecting it. And here is a link I found describing it. (Take note the reference to Melchizedek, corresponds to the teaching about Jesus in the New Testament book of Hebrews).