Yes- he said he "was" God at John 1:1, as He did of Moses at Ex 7:1, of the Judges of Israel, angels - and even Satan.
(These either SPOKE for Him, or pretended to BE Him)
The context of the chapter, book, and ENTIRE BIBLE shows this.
The OP asks a question, but it should really read, How did the Father define the Son?
Paul states, under inspiration of the Holy Ghost (2 Timothy 3:16; 2 Peter 1:21), citing the OT inspired and preserved texts (Psalms 12:6-7)
Heb 1:8 But unto the Son he saith (citing Psalms 45:6-7), Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom.
Heb 1:9 Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows.
Heb 1:10 And (the Father is still speaking unto the Son, Paul continues citing Psalms 102:12,22,25-27), Thou, Lord (JEHOVAH Immanuel), in the beginning hast laid the foundation of the earth; and the heavens are the works of thine hands:
Heb 1:11 They shall perish; but thou remainest; and they all shall wax old as doth a garment;
Heb 1:12 And as a vesture shalt thou fold them up, and they shall be changed: but thou art the same, and thy years shall not fail.
Heb 1:13 But to which of the angels said he at any time, Sit on my right hand, until I make thine enemies thy footstool?
The Son, is "God" and "Lord" (JEHOVAH Immanuel, citing Psalms 102), being "the same".
Psalms 102:12 KJB - But thou, O LORD, shalt endure for ever; and thy remembrance unto all generations.
Side note, “... O LORD ...” [Psalms 102:12 KJB] is direct reference to JEHOVAH the Son, see Psalms 102:1,12,15,16,19,21,22 KJB:
Psalms 102:12 (102:13) HOT [read from Right to Left] -
ואתה יהוה לעולם תשׁב וזכרך לדר ודר׃
Side note, in the so-called LXX [*Septuagint, the work of Origen in his Hexapla, not the work of 70 or 72 Jewish scholars from the twelve tribes, and definitely not written before AD 100], notice how it translates the Hebrew JEHOVAH into the Greek “κύριε”, “kurie” or English “LORD”, which is used to identify Jesus Christ throughout the New Testament.
Psalms 102:12 (101:13) LXX* - σὺ δέ, κύριε, εἰς τὸν αἰῶνα μένεις, καὶ τὸ μνημόσυνόν σου εἰς γενεὰν καὶ γενεάν.
Paul continues this thought in Hebrews 13:
Hebrews 13:5 KJB - Let your conversation be without covetousness; and be content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee.
Hebrews 13:6 KJB - So that we may boldly say, The Lord is my helper, and I will not fear what man shall do unto me.
Hebrews 13:7 KJB - Remember them which have the rule over you, who have spoken unto you the word of God: whose faith follow, considering the end of their conversation.
Hebrews 13:8 KJB - Jesus Christ the same yesterday, and to day, and for ever.
As it is written:
Malachi 3:6 KJB - For I am the LORD, I change not; therefore ye sons of Jacob are not consumed.
Psalms 102:27 KJB - But thou art the same, and thy years shall have no end.
Thus Jesus is
"I AM", unchanging Person/Being of the Son, who sits at the right hand of the Father on the Throne of Eternal Deity and all the angels of God worship Him (See NWT (1970; Green Hardback) Hebrews 1:6).
John the Baptist (whose testimony is from Heaven) said:
Joh_1:15 John bare witness of him, and cried, saying, This was he of whom I spake, He that cometh after me is preferred before me: for he was before me.
Joh_1:27 He it is, who coming after me is preferred before me, whose shoe's latchet I am not worthy to unloose.
Joh_1:30 This is he of whom I said, After me cometh a man which is preferred before me: for he was before me.
Jesus pre-existence, even "before all things":
Joh 1:3 All things were made by him; and without him was not any thing made that was made.
See Genesis 1.
"God said" (Father), "God made" (Son, in loving response to the Father's will), "
God saw" and "moved" (Holy Ghost/Spirit).
Joh 1:10 He was in the world, and the world was made by him, and the world knew him not.
Joh 1:11 He came unto his own, and his own received him not.
Who came unto His own? The Son, JEHOVAH Immanuel on behalf of the Father (JEHOVAH, Ancient of Days) ... For the Son had taken the people out of Egypt and was with them all the time in the cloud and in the fire. Thus the Son says, I AM with you alway, to lead you, to guide you, to be the rereward (rear guard). He is my help:
Mat_15:25 Then came she and worshipped him, saying, Lord, help me. (Hebrews 13:6, etc)
The passage in Hebrews 3, in regards Christ and Moses, is speaking of the superiority of the Son (Deity (eternal and uncreated) by nature), over the servant (Moses, creature by nature). Jesus is the Apostle of the Father.
Heb 3:1 Wherefore, holy brethren, partakers of the heavenly calling, consider the Apostle and High Priest of our profession, Christ Jesus;
The Son is the eternal "fellow" of the Father, ever having sat at His (the Father's) right hand on and in the Throne of Eternal Deity:
Zec_13:7 Awake, O sword, against my shepherd, and against the man that is my fellow, saith the LORD of hosts: smite the shepherd, and the sheep shall be scattered: and I will turn mine hand upon the little ones.
Continuing:
Heb 3:4 For every house is builded by some man; but he that built all things is God.
Heb 3:5 And Moses verily was faithful in all his house, as a servant, for a testimony of those things which were to be spoken after;
Heb 3:6 But Christ as a son over his own house; whose house are we, if we hold fast the confidence and the rejoicing of the hope firm unto the end.