The answer to the question non contextually is, the same word beginning or the first or at the start αρχη is used identically in the rest of John’s account of the gospel.
Which beginning does this refer to? It refers to the beginning of Creation, that beginning. So we now have a time stamp. (If it’s not obvious enough that it’s referring to the very beginning consult v3 that says ALL, with the exclusion of nothing. That is the beginning as per Genesis 1:1, prior to it was no heaven, no earth, no heavenly beings because there was no heaven to exist in, only God who is uncreated and without beginning)
So therefore at the beginning of Creation there was God and there was God the Word
He the Word was with God at that very beginning v2
Now to add OT context to what John was describing. John is saying that this Word has a beginning, but being the Word is God, God is without beginning. Therefore this Word is God in a new form
“And now, Father, glorify me in your own presence with the glory that I had with you before the world existed.”
“Father, I desire that they also, whom you have given me, may be with me where I am, to see my glory that you have given me because you loved me before the foundation of the world.”
He had a glory which He no longer has in the aftermath of His begetting
All things were made by the Word, therefore nothing existed prior to the Word in the natural and supernatural world (God being outside of His own Creation and God the Word now about to make Creation)
“All things were made through him, and without him was not any thing made that was made.”
All things were made through Him the Word, meaning it HAS to be speaking about day one of Creation, there was no heaven or earth prior to day one (circa 4930 earlier)
The Word was begotten, but when?
“but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world.”
The Son had to have been begotten prior to the creation otherwise it would not have been created through Him.
“He is the image of the invisible God, the firstborn of all creation.”
He in the form that He took as the Word, the Son, the one through whom all things were Created, the image/imager/representative of God, the Angel of the Lord, one with less glory after the begetting, the archon or the first of all Creation, in this form He remained fully God but took on a lower position by identifying with Creation at the Beginning and being it’s Creator, interacting with His Creation,
And He went one step even further and humbled Himself by becoming a human, going from the supernatural heavenly body of the Angel of the Lord, the Visible God of the OT, into the biological machinery called the human body.
Yes in the beginning being at the first or the first occurrence or the beginning in English. And John makes it ABUNDANTLY clear that the Word WAS GOD even at the beginning.
In the English people argue that the World (meaning the cosmos/universe) was not made by Him but through δι Him, in other words He wasn’t the agent of Creation just the medium, but in the Greek the word δι needs to be understood even if you want to translate it through, that at the source HE is the Creator
Colossians 1:16 says that by εν Him were all things made and through δι Him and that they were made for εις Him.
The Earth is His, made for Him and the Earth belongs to the Lord
“The earth is the Lord’s יהוה and the fullness thereof, the world and those who dwell therein,”
Yes it the word beginning refers to the very first second of time and thereafter, Yes the Word was there at that beginning and Yes the Word was God