Wow. How much time do you have? LOL. There is simply way too much proof to list here.
Dr. Michael Brown does an excellent job of providing proof and answers in his five-volume series “Answering Jewish objections to Jesus.” 
But for a quick answer…. We believe Jesus fulfilled the prophecies of the “suffering servant” that God promised the Jewish people who would come one day.
God told the Jewish people what to look for in the suffering servant (another name for the Messiah.) Not meaning at all “Look for someone who is six feet tall and weighs 180 lbs.” Not at all.
But God gave Israel certain prophecies about the Messiah scattered in the Hebrew Bible and it does require a little bit of work to look all of them up.
The first place to start is Isaiah chapter 53. This passage is about the suffering servant and was looked at by ancient Rabbis as the Messiah.
Ancient rabbinical writings always looked at Isaiah chapter 53 as a reference to the coming Messiah. Here are just a few of many many examples –
Babylonian Talmud: “The Messiah –what is his name?…The Rabbis say, The Leper Scholar, as it is said, `surely he has borne our griefs and carried our sorrows: yet we did esteem him a leper, smitten of God and afflicted…'” (Sanhedrin 98b)
Midrash Ruth Rabbah: “Another explanation (of Ruth ii.14): — He is speaking of king Messiah; `Come hither,’ draw near to the throne; `and eat of the bread,’ that is, the bread of the kingdom; `and dip thy morsel in the vinegar,’ this refers to his chastisements, as it is said, `But he was wounded for our transgressions, bruised for our iniquities‘”
“This refers to the King Messiah. And why does he call him `the great mountain?’ because he is greater than the patriarchs, as it is said, `My servant shall be high, and lifted up, and lofty exceedingly’ –he will be higher than Abraham…lifted up above Moses…loftier then the ministering angels…” (Quoted in The Fifty-third Chapter of Isaiah According to the Jewish Interpreters, Ktav Publishing House, 1969, Volume 2, page 9.)
It is only an invention of the modern Jewish writers (from Rashi on…) who claim that Isaiah 53 is national Israel.
(For more on this visit our article here - What ancient Rabbis have said about Isaiah chapter 53)
(Also this - Ten reasons why Isaiah 53 is not about Israel)
So what else is there that points to Messiah…. Well, according to the Jewish Bible Messiah would be…
- Born in Bethlehem….. The Jewish prophet said so in Micah 5:2
- Reach many in Galilee….. The Jewish prophet said so in Isaiah 9:1
- Born a descendant of David….. The Jewish prophet said so in 2 Samuel 7:12-13
- Do miracles like Moses….. The Jewish prophet said so in Deuteronomy 18:18
- Enter Jerusalem on a donkey….. The Jewish prophet said so in Zechariah 9:9
- Arrive after King David died….. The Jewish prophet said so in 2 Samuel 7:12-13
- A rejected man……. The Jewish prophet said so in Isaiah 53:3
- Die as a substitute for others….. The Jewish prophet said so in Isaiah 53:5
- Be pierced………………… The Jewish prophet said so in Zechariah 12:10
- Rise from the dead…… The Jewish prophet said so in Isaiah 53:10
- Have followers from all nations…… The Jewish prophet said so in Daniel 7:14
And even MORE important…………..
- Messiah was to arrive BEFORE The Temple was destroyed in 70 C.E….. See -> Daniel 9:26
- Messiah was to have an impact on all nations….. The Jewish prophet said so in Isaiah 49:6
- Messiah was to ‘sprinkle’ many Nations….. The Jewish prophet said so in Isaiah 52.15 and used the Hebrew concept in Leviticus (Lev. 16.14) of the sprinkling of the blood of atonement. Moses did as well (Exodus 24:8)
If this is not Jesus — who else could it be?
And this is just the start…..
The list goes on and on,
There is not a shadow of doubt – Yeshua (Jesus in Hebrew) was/is the Messiah of Israel.
