What evidence do we have that Old Testament prophecies we believe to be Messianic Prophecies are also considered to be Messianic Prophecies by the Jewish people? And if our versions of them are the same what is their reasoning for not accepting Jesus?
The evidence that both are the same is that we’re both reading the same Scripture. We call it the Old Testament.
At the time the Lord came, Israel didn’t understand that there were two comings and was looking for the fulfillment of what we now call 2nd Coming prophecies. Since Jesus didn’t fit these prophecies, they didn’t recognize Him as their Messiah.
Many in our day will make the same mistake in reverse. They’ll be looking for the Lamb of God, the gentle Jesus of the first coming, and won’t recognize the Lion of Judah Who rules with an iron scepter of the second.