It's more important how the word is used in its syntax than taking the same word in a completely different context. For example we should look at what the word means when it refers to a person and also when it is the head noun of a genitive phrase like Revelation 3:14.
BDAG says for linguistic reasons it is probable that it means first-created. Here is why:
When a verbal noun is the head noun of a genitive it is either a subjective genitive or objective genitive. This is pretty basic Greek 101. That is what we find with "beginning of creation.
So convert the noun to a verb and the genitive is the subject or object. In this case it is "God created."
The Son is the beginning of what God created.
Interestingly Wisdom at Proverbs 8:22 in the LXX also the αρχή of what God created and also it/he explicitly says "God created me the beginning of his works." I am not arguing that the Word is Jesus here so much as to show the same syntax. However many so see an allusion from Proverbs 8:22 to Revelation.
Be that as it may, you do seem to agree that it does not mean "origin" at 3:14. And since it does not mean origin at John 1:1, you are left with no opinion still?
It's not difficult to understand when we reconcile all scriptures without sweeping some scriptures under the carpet from a biased theological background.
John in his gospel and Epistles says that no one has ever seen God at anytime. Apostle Paul goes further to say that immortal God dwells in unapproachable light Whom no one has seen nor can see - 1Tim 6.
Yet OT fathers and prophets have seen Him face to face. Is there a contradiction? Of course Not! Some traditional theologians say those appearances were theophanies. In reality they are not!
What John and Paul mean is that no one can see God in form of Spirit as He is transcendent, invisible, unapproachable and can't be heard.
Yahusha/Yeshua testifies to the unbelieving Jews (not believing in the Son) that they (OT) have never seen Father's form nor have heard His voice.
John 14 addressing to Philip, The Son says that those who have seen Him have seen The Father.
If anyone doesn't know The Son, can't possibly know The Father as He is His visible face. Who is The WORD? The WORD is the One Who interacts with the creation where the creation can hear, see and handle - 1John 1:1.
Jacob wrestled with a Man - face of God - 'PENIEL'.
This visible concept is revealed in the OT:
Exod 15:3
“יהוה is a man of battle, יהוה is His Name.
Isaiah 42:13 יהוה goes forth like a mighty man. He stirs up ardour like a fighter. He cries out, yes, shout aloud. Over His enemies He shows Himself mighty.
Ezk 1:26 And above the expanse over their heads was the likeness of a throne, in appearance like a sapphire stone. And
on the likeness of the throne was a likeness as the appearance of a man high above it.
28:
As the appearance of a rainbow in a cloud on a rainy day, so was the appearance of the brightness all around it.
This was the appearance of the likeness of the esteem of יהוה. And when I saw it, I fell on my face, and I heard a voice of One speaking.
YHWH reveals Himself in duality of powers in the OT.
It is quite evident in Gen 1:26 - Let US make man.
It's also in the perspective of the Gospel message:
Gen 1:3 - 'Let there be Light'
Look at how Paul interprets this passage in 2Cor 4: 6:
For God, who commanded the light to shine out of darkness, hath shined in our hearts, to
give the light of the knowledge of the glory of God in the face of Jesus Christ (kjv).
It's quite obvious when God in His Spirit form can't be seen or heard - He has His own face in YHWH - revealed in duality of powers.
The One Who spoke as The Father in OT is now The Son of God come in likeness of sinful flesh. Phil 2:5-7 teaches that His nature of being God has not changed as He is equal with God but didn't hold on to this reputation as He made Himself a Servant for the sake of His people whom He came to save and give them right to sonship and make them joint heirs with Him.
Paul in Colossians says He the image of the invisible God (Gen 1:26 - Let US make man) and the Firstborn of all creatures (old creation) as well as the Firstborn from the dead (new creation). In Him all things consist.
He is our YHWH Who became our Yeshuah - Isaiah 12:2.
In Rev 21:3 - Tabernacle of God is in midst of His people where they will see Him face to face.
At first time He as The Word becoming flesh Tabernacled in midst of His people but majority of them didn't recognize their God as He came down to the earth. This is a precursor to Rev 21:3.