You have a misunderstanding of what "only begotten" (monogenes) means.
Mono
Gene
Mono is simply "one", "only".
Mono is used in conjunction or connection, gene.
Gene refers to race or nature (that which makes up the content of essence), that which comes about or exists through/from another.
It's used this way even coming down to our English:
"gene (n.) 1911, from German Gen, coined 1905 by Danish scientist Wilhelm Ludvig Johannsen (1857-1927), from Greek genea "generation, race" (from PIE root *gene- "give birth, beget"). De Vries had earlier called them pangenes. Gene pool is attested from 1946." -
https://www.etymonline.com/word/Gene
That is why the Father is called:
monon alethinon theon, ton theon
And because the Son is in the express image of the Father, is called:
monogene, logos en o theos
The Father's nature is His own, underived ("true"*), but the Son, because He is the Son has that same nature because of the Father.
True -
https://www.thesaurus.com/browse/true
Authentic -
https://www.thesaurus.com/browse/authentic
Original -
https://www.thesaurus.com/browse/original
It means underived.
So monogene in connection with monon alethinon theon means that the nature of the Son is of the Father and he is the only Son of the Father with that nature of the Father.
Created Angels and humans are sons, but not of that same nature as the Father and Son are.
In other words:
The Father is "The only true (underived in nature) God"
The Son is "The only begotten (derives His nature from the Father because He is the Son) God"
Remember, "only begotten" has nothing to do with time, or creation, or coming into existence in these contexts, but and only deals with the existing nature of the Son in relation to the Father.
I know what people think when I say that, but they need to understand the definition of what is said by saying it.
JEHOVAH Elohiym is the eternal family/relationship. JEHOVAH is the singular eternal family name, while Elohiym (Gods, trio) are the individual Persons/Beings that exist in that eternal family/relationship, Matt. 28:19; 1 Jhn. 5:7,8.
1. JEHOVAH, "the LORD" (Gen. 19:24b.; Zec. 3:2b.), "the Ancient of days" (Dan. 7:9,13,22) is "the only true God" (Jhn. 17:3; τὸν μόνον ἀληθινὸν θεὸν), "God" (Jhn. 1:1b.; τὸν θεόν), "thy God" (Heb. 1:9; ὁ θεός σου), "God the Father" (2 Jhn. 1:3; θεοῦ πατρός) the "person" (Job 13:8; Heb. 1:3) identified in the beginning as the "God said" (Gen. 1:6), for it was by Him that Revelation says, "Thou art worthy, O Lord, to receive glory and honour and power: for thou hast created all things, and for thy pleasure they are and were created." (Rev. 4:11).
2. Jesus JEHOVAH (Gen.49:18; Exo. 14:13; 2 Chr. 20:17; Jon. 2:9; Psa. 119:174 HOT) or JEHOVAH Immanuel (see Psa. 46:7,11 HOT)), "the LORD" (Gen. 19:24a.; Zec. 3:2a.), "the son of man" (Dan. 7:13), "the only begotten" (Jhn. 1:14,18, 3:16,18; Heb. 11:17; 1 Jhn. 4:9, is basically monogene (μονογενῆ; Jhn. 3:16; Heb. 11:17; 1 Jhn. 4:9) or monogenes (μονογενὴς; Jhn. 1:18) or monogenous (μονογενοῦς; Jhn. 1:14, 3:18)), "the Lord Jesus Christ, the Son of the Father" (2 Jhn. 1:3; Κυρίου Ἰησοῦ Χριστοῦ τοῦ υἱοῦ τοῦ πατρός) is not "the only true God" (Jhn. 17:3), but is "the express image of his person" (Heb. 1:3; χαρακτὴρ τῆς ὑποστάσεως αὐτοῦ), being "the Word was God" (Jhn. 1:1c.; θεὸς ἦν ὁ λόγος), who is "O God" (Heb. 1:9; ὁ θεός), the "just person" (Matt. 27:24, "person", 2 Cor. 2:10) indentified in the beginning as "God made" (Gen. 1:7) on behalf of the Father's direction (Pro. 8:22-36; Exo. 20:12), for it was by him (the Son) that John says, "All things were made by him; and without him was not any thing made that was made." (Jhn. 1:3), that Ephesians says, "And to make all men see what is the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ:" (Eph. 3:9), that Colossians says, "For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him:" (Col. 1:16), that Hebrews says, "Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;" (Heb. 1:2), the very, "I AM THAT I AM" (Exo. 3:14), the great "I am" (Jhn. 8:58; ἐγὼ εἰμί), the very "fellow" (Zec. 13:7) of the Father's person, and who comes in the name of His Father (Jhn. 5:43).
3. The Holy Spirit of JEHOVAH (Luk. 4:18), "his Spirit" (Isa. 48:16), "the LORD" (Zec. 3:2c.), the "another Comforter" (Jhn. 14:6), even "he", "the spirit of truth" (Jhn. 14:17, 15:26, 16:13), "God" (Acts 5:4), identified in the beginning as "the Spirit of God moved" (Gen. 1:2) and "God saw" (Gen. 1 throughout, the eternal Witness who inspired the scriptures; 2 Tim. 3:16-17; 2 Pet. 1:21), by which/whom everything is "created" (Psa. 104:30) and "made" (Job 33:4), whose nature is a mystery left unspoken of in scripture, but is the person who does "not speak of himself" (Jhn. 16:13), but comes in the name of the Son (Jhn. 14:26).
The eternal Heavenly Trio - family JEHOVAH Elohiym, over all creation as "Godhead".