One cannot know for certain what the Pharisees of Jesus’ day ascribed to or what motivated them beyond money and power but they appeared well versed in the Scriptures, in so far as what they said, even if they had their own prejudicial expectation.
When Herod at the time of Jesus’ birth asked for information he received it most accurately.
“When Herod the king heard this, he was troubled, and all Jerusalem with him; and assembling all the chief priests and scribes of the people, he inquired of them where the Christ was to be born.”
Matthew 2:3-4
Which could lead one to assume that within a thirty year period some of the scholars who answered Herod were still around to explain who the Messiah was and details about Him from the Scriptures to the leaders thirty years later.
“They told him, “In Bethlehem of Judea, for so it is written by the prophet: “‘And you, O Bethlehem, in the land of Judah, are by no means least among the rulers of Judah; for from you shall come a ruler who will shepherd my people Israel.’””
Matthew 2:5-6
This points to the fact that that they expected the ruler, the king, the anointed one, the one from the line of David to be BORN, in other words a human being.
And this human was also a pre-existent being who would enter into humanity having had a previous existence
“But you, O Bethlehem Ephrathah, who are too little to be among the clans of Judah, from you shall come forth for me one who is to be ruler in Israel, whose coming forth is from of old, from eternity. Therefore he shall give them up until the time when she who is in labor has given birth; then the rest of his brothers shall return to the people of Israel. And he shall stand and shepherd his flock in the strength of the Lord, in the majesty of the name of the Lord his God. And they shall dwell secure, for now he shall be great to the ends of the earth.”
Micah 5:2-4
This makes reference again to the birth of a ruler, a Shepherd, the anointed.
It is also important to note that scholars who studied in-depth the Holy Scriptures noticed in the prophets that God has a son, who is distinct from the sons of God.
“I will tell of the decree: The Lord said to me, “You are my Son; today I have begotten you. Ask of me, and I will make the nations your heritage, and the ends of the earth your possession. You shall break them with a rod of iron and dash them in pieces like a potter’s vessel.””
Psalm 2:7-9
These are Scriptures used by NT writers to show that Jesus was that Son. Jesus Himself asserts He is He.
“The one who conquers and who keeps my works until the end, to him I will give authority over the nations, and he will rule them with a rod of iron, as when earthen pots are broken in pieces, even as I myself have received authority from my Father.”
Revelation 2:26-27
It would seem out of place for the ancients Jews to accept these prophecies if they were monotheists, but they believed in a visible God and an invisible God. Jesus makes the point that only He has seen the Father, which implies that the God men saw in the OT was not the Father but another.
“Kiss the Son, lest he be angry, and you perish in the way, for his wrath is quickly kindled. Blessed are all who take refuge in him.”
Psalm 2:12
Again the reference to the Son. Specifically THE son of God.
This is not the only reference and in true keeping with a witness of minimum two or three witnesses there is another passage that makes reference to the son, specifically of God.
“Who has ascended to heaven and come down? Who has gathered the wind in his fists? Who has wrapped up the waters in a garment? Who has established all the ends of the earth? What is his name, and what is his son’s name? Surely you know!”
Proverbs 30:4
Again to an astute careful reader this detail does not go unnoticed.
God clearly has a son
The messiah was going to be born, therefore would be a human.
What maybe no one had connected yet, was that the Messiah would be the visible God taking on the human biological machine/body.
In conclusion, I cannot speak to why Jesus was asked this question in this way. But Jesus tried very hard to help them connect the dots, which in my mind tells me they knew the Messiah would be God and would be born and would be THE Son of God.
“So the Jews gathered around him and said to him, “How long will you keep us in suspense? If you are the Christ, tell us plainly.” Jesus answered them, “I told you, and you do not believe. The works that I do in my Father’s name bear witness about me,”
John 10:24-25
At least believe because you know the Messiah would cast out demons, the single sign that was not practiced in the OT and they still refused to believe.
My best guess is they knew what they should expect, EVEN the exact TIME according to Daniel’s prophecy when He should appear, which corresponded to the 100th Jubilee year from day 1 of creation, the year 4,900. But they just could not see, because their eyes were darkened by the love of money and greed.
Imagine how blind you have to be, to know the truth, to understand the prophecies, to have Truth incarnate before you and to stumble over Him.
“Why? Because they did not pursue it by faith, but as if it were based on works. They have stumbled over the stumbling stone, as it is written, “Behold, I am laying in Zion a stone of stumbling, and a rock of offense; and whoever believes in him will not be put to shame.””
Romans 9:32-33