And he took the book of the covenant, and read in the audience of the people: and they said, All that the LORD hath said will we do, and be obedient. - Exodus 24:7
Although not explicitly stated as the OP inquires after, the implicit sense is certainly present that when what the Lord has said is written down and then read aloud, that which is heard is that which God has spoken no less than when it is heard directly, or when a prophet hears the word of God and speaks, "Thus saith the Lord.".
The giving of the Law was a process more than an event and the formal beginning of the process is in Exodus and includes all three aspects:
And Moses went up unto God, and the LORD called unto him out of the mountain, saying, Thus shalt thou say to the house of Jacob, and tell the children of Israel; Ye have seen what I did unto the Egyptians, and how I bare you on eagles' wings, and brought you unto myself. Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine: And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel. And Moses came and called for the elders of the people, and laid before their faces all these words which the LORD commanded him. And all the people answered together, and said, All that the LORD hath spoken we will do. And Moses returned the words of the people unto the LORD. - Exodus 19:3-8
Moses was then instructed to prepare the people to witness and hear the Lord coming down to speak with him:
And the LORD said unto Moses, Lo, I come unto thee in a thick cloud, that the people may hear when I speak with thee, and believe thee for ever. And Moses told the words of the people unto the LORD. And the LORD said unto Moses, Go unto the people, and sanctify them to day and to morrow, and let them wash their clothes, And be ready against the third day: for the third day the LORD will come down in the sight of all the people upon mount Sinai. - Exodus 19:9-11
The people prepared themselves as God instructed through Moses and brought them out of the camp to Mount Sinai. Moses then went up the mountain and God spoke with him. There was fire, smoke, tremblings, etc., and the people were terrified. Moses was told to go down and speak to the people so that they would not attempt to "break through" and perish (Exodus 19:16-25).
In Exodus 20:1-17 Moses speaks to Israel the "ten commandments" and the people respond fearfully by asking permission to leave God's presence and have Moses mediate (incidentally, this was God's spoken purpose for this scene given in 19:9):
And all the people saw the thunderings, and the lightnings, and the noise of the trumpet, and the mountain smoking: and when the people saw it, they removed, and stood afar off. And they said unto Moses, Speak thou with us, and we will hear: but let not God speak with us, lest we die. And Moses said unto the people, Fear not: for God is come to prove you, and that his fear may be before your faces, that ye sin not. And the people stood afar off, and Moses drew near unto the thick darkness where God was. - Exodus 20:18-21
From this point through chapter 23 is the fleshing out of the Law as summarized by the 10 commandments which concludes in a promise concerning the land of Canaan. In Exodus chapter 24 the covenant is confirmed:
And he said unto Moses, Come up unto the LORD, thou, and Aaron, Nadab, and Abihu, and seventy of the elders of Israel; and worship ye afar off. And Moses alone shall come near the LORD: but they shall not come nigh; neither shall the people go up with him.
And Moses came and told the people all the words of the LORD, and all the judgments: and all the people answered with one voice, and said, All the words which the LORD hath said will we do. - Exodus 24:1-3
This establishes well that the people, hearing what the mediator says, receive those words as "All the words which the Lord has said" even though it is second hand to them. The next thing that Moses does is to write down all of what God had spoken to him and read it in the hearing of the people. The response of the people is exactly the same:
And Moses wrote all the words of the LORD, and rose up early in the morning, and builded an altar under the hill, and twelve pillars, according to the twelve tribes of Israel. And he sent young men of the children of Israel, which offered burnt offerings, and sacrificed peace offerings of oxen unto the LORD. And Moses took half of the blood, and put it in basons; and half of the blood he sprinkled on the altar.
And he took the book of the covenant, and read in the audience of the people: and they said, All that the LORD hath said will we do, and be obedient. - Exodus 24:4-7
I think that this constitutes the first instance of a continuing pattern throughout Scripture where that which God has spoken is rightly received as the "Word of God" by the direct hearer as well as by those to whom that Word is passed on either orally or in written form.
Thus it is fair to say that the already established portions of the written Word would rightly be considered as the Word of God even while what we now know to be the completed canon was still yet to be. This is born out in Jesus' response to the Tempter where the strongest correlation is drawn between what is written and what God speaks:
It is written, Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God. - Matthew 4:4
While the Bible never calls itself "the Word of God" in the sense that some Christians will that title is certainly in keeping with the whole tenor of God's revelation unto us.