When is the phrase "Word of God" first used to refer to the Scriptures?

The expression "word of God" (Hebrew "dabar elohim/דְּבַ֥ר אֱלֹהִֽים") seems to be first used by Samuel.

And as they were going down to the end of the city, Samuel said to Saul, Bid the servant pass on before us, (and he passed on), but stand thou still a while, that I may show thee the word of God. (1 Samuel 9:27, KJV)

The expression was further used by the scribes afterward.

But the word of God came unto Shemaiah the man of God, saying, (1 Kings 12:22, KJV)

And it came to pass the same night, that the word of God came to Nathan, saying, (1 Chronicles 17:3, KJV)

And then a similar expression was used by Solomon, in a more poetic sense.

Every word of God is pure: he is a shield unto them that put their trust in him. (Proverbs 30:5, KJV)

Proverbs 30:5 uses a different Hebrew expression which was translated as "every word of God." This may, however, have influenced Jesus' own expressions during the temptations in the wilderness.

And Jesus answered him, saying, It is written, That man shall not live by bread alone, but by every word of God. (Luke 4:4, KJV)

Jesus quoted from Deuteronomy 8:3 which, in Hebrew, does not have the word "word" (dabar)--so it could perhaps have been translated as "every thing that proceeds from the mouth of God."

Conclusion

Though Moses used a related expression, the actual "word of God" expression seems to have first been used by Samuel, as far as the Bible records. But the scribes, shortly thereafter, used it to refer to past instances of the word of God having been given or expressed.

OP: I am asking specifically about the origin of using the phrase "word of God" to refer to the Bible.

The first reference to "word of the LORD" is here.

After these things the word of the LORD came unto Abram in a vision, saying, Fear not, Abram: I am thy shield, and thy exceeding great reward. Gen 15:1

The first reference to "word of God" is here.

And as they were going down to the end of the city, Samuel said to Saul, Bid the servant pass on before us, (and he passed on,) but stand thou still a while, that I may shew thee the word of God. 1 Sam 9:27

When do these phrases refer to the Bible, the written word of God, rather than the spoken word of God? Basically, the two ideas of spoken and written are the same. Like the New Testament, the apostles spoke and then wrote it down.

Making the word of God of none effect through your tradition, which ye have delivered: and many such like things do ye. Mark 7:13

Jesus Christ declares here that the Old Testament is the word of God. The valid prophets spoke "thus sayeth the LORD". They spoke as God moved them, not sourcing their speech to themselves.

Luke puts it this way.

Then the twelve called the multitude of the disciples unto them, and said, It is not reason that we should leave the word of God, and serve tables. Acts 6:2

Peter puts it this way.

Knowing this first, that no prophecy of the scripture is of any private interpretation. For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost. 2 Peter 1:20-21

In short, God spoke through valid prophets who wrote these things to leave us a record. Likewise, Christ, the Word, also left valid witnesses who wrote a record. This is the 66-book Bible.

Lastly, there is a distinction between the two Greek words logos and rhema that are typically translated "word".

The significance of rhema (as distinct from logos) is exemplified in the injunction to take "the sword of the Spirit, which is the word of God," Eph 6:17; here the reference is not to the whole Bible as such, but to the individual scripture which the Spirit brings to our remembrance for use in time of need, a prerequisite being the regular storing of the mind with Scripture. BlueLetterBible

The idea is that the logos is the spoken word of God that came to be written down and the rhema is the application of the logos, the written word.

TO ADD: A diminutive of logos is logion. It is translated as oracle.

Oracle: a diminutive of logos, "a word, narrative, statement," denotes "a Divine response or utterance, an oracle;" it is used of (a) the contents of the Mosaic Law, Act 7:38; (b) all the written utterances of God through OT writers, Rom 3:2; (c) the substance of Christian doctrine, Hbr 5:12; (d) the utterance of God through Christian teachers, 1Pe 4:11.

Notes: Divine "oracles" were given by means of the breastplate of the High Priest, in connection with the service of the tabernacle, and the Sept. uses the associated word logeion in Exd 28:15, to described the breastplate. -source-

Additionally, there is a broader description that points to the same idea of words spoken by God being the written words of God.

In the N. T. spoken of the words or utterances of God: of the contents of the Mosaic law, Acts 7:38; with τοῦ Θεοῦ or Θεοῦ added, of his commands in the Mosaic law and his Messianic promises, Romans 3:2, cf. Philippi and Umbreit at the passage; of the substance of the Christian religion, Hebrews 5:12; of the utterances of God through Christian teachers, 1 Peter 4:11. (In ecclesiastical writings λόγια τοῦ κυρίου is used of Christ's precepts, by Polycarp, ad Philipp. 7, 1 [ET]; κυριακα λόγια of the sayings and discourses of Christ which are recorded in the Gospels, by Papias in Eusebius, h. e. 3, 39; Photius c. 228, p. 248 (18 edition, Bekker); (τά λόγια τοῦ Θεοῦ) of the words and admonitions of God in the sacred Scriptures, Clement of Rome, 1 Cor. 53, 1 [ET] (where parallel with αἱ ἱεραι γραφαί), cf. 62, 9 [ET]; (and τά λόγια simply, like αἱ γραφαί of the New T. in the interpolated Epistle of Ignatius ad Smyrn. 3 [ET]). Cf. Schwegler ((also Heinichen)), Index 4 ad Eusebius, h. e. under the word λόγιον; (especially Sophocles Lexicon, under the word and Lightfoot in the Contemp. Rev. for Aug. 1875, p. 399ff On the general use of the word cf. Bleek, Br. a. d. Hebrew iii., pp. 114-117).) THAYER’S GREEK LEXICON, Electr -ibid

Note the subsequent references to the New Testament from the writings of Polycarp, Clement, Papias, and others.

So, to answer the OP, the usage of "word of God" or "word of the Lord" or "oracles of God" first appears from Christ as He applies the written word sourced to God versus the spoken tradition from men. It then appears throughout the New Testament and into the very early church fathers.

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.