It is only Christians AFTER the fact that put together Isaiah's suffering servant verses and the Messiah. Only after the Resurrection event. Apparently, the message of God's Salvation plan was foretold in hidden ways.
Regards
The prophet told them the time of the coming of the Messiah. The leaders of the people kept it from them. Jesus was angry with the leaders for this very reason, and told them so. Because they did not know the time of their visitation, their temple was destroyed and they were dispersed, just as Moses told them they would be. They had no excuse, none of them.