In Matthew 2 it becomes obvious people knew Jesus was going to fulfill the over 300 descriptions of the promised messiah in the Old Testament.
1 Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, magi from the east arrived in Jerusalem, saying, 2 “Where is He who has been born King of the Jews? For we saw His star in the east and have come to worship Him.” 3 When Herod the king heard this, he was troubled, (Why?, there is a new king) and all Jerusalem with him. 4 Gathering together all the chief priests and scribes of the people, he inquired of them where the Messiah was to be born. 5 They said to him, “In Bethlehem of Judea; for this is what has been written by the prophet: 6 ‘AND YOU, BETHLEHEM, LAND OF JUDAH, ARE BY NO MEANS LEAST AMONG THE LEADERS OF JUDAH; FOR OUT OF YOU SHALL COME FORTH A RULER WHO WILL SHEPHERD MY PEOPLE ISRAEL.'”
The chief priests, the scribes, the magi, Herod the king, all knew Jesus was fulfilling the promise of a coming messiah. Later on in Matthew 2 King Herod even issues a decree to have all children 2 years and under in Bethlehem killed because he knew the promises had been fulfilled in Jesus. A new king was coming!
So how did they miss it?