First of all, have you looked at an interlinear for John 1:3, because not all translations agree. Some say 'made,' and others say 'created.' Yet the definition of the Greek doesn't give a real good explanation. And to say that nothng was made (or some say, created) without the Word does not mean that the Word did not have a beginning. It means that the Word made everything other than himself. He didn't make himself. In fact, putting it all together, it says, "Through him all things were made; without him nothing was made that has been made." So through him (the Word - Jesus) all things were made, "without him nothing was made that has been made" tells us that without the Word nothing was made.
John 1:1-4 is something like this for most translations. It is rather emphatic in verse 3 that nothing that has been made without the Word's participation.
The NWT takes away the emphatic nature of verse 3 by joining "that has been made" on to verse 4 to created a sentence that does not make much sense really, and it does not change the meaning of what verse 3 tells us, just takes away some of it's emphatic nature. I guess that is good for the WT and makes them think that they can now say that the Word was also made,,,,,,,,,,,,,,but it doesn't do that at all. It still means that every little or big or material or spiritual thing that was made/brought into existence, was brought into existence through the Word.
Your reasoning seems to be illogical and a way of denying what is written there.
NIV John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was with God in the beginning. 3 Through him all things were made; without him nothing was made that has been made. 4 In him was life, and that life was the light of all mankind.
NWT John 1........What has come into existence 4 by means of him was life, and the life was the light of men.
So there were TWO at the beginning of what was made. God and the Word. Two. And everything that was made was made through the word. "Without him" tells there was one (God Almighty) that did not 'make things' without the Word. (That's two.) Sensible thinking tells us that it means what came after the Word.
Further, it doesn't say there were three persons there "at the beginning," each without beginning. It doesn't say that at all.
Yes there were 2 at the beginning of what was made. The God and the Word were both there already before anything was made. Now you seem to be getting it. The Word certainly was not another god and He was not "the God". I could try to explain John 1:1 but I think the best way to go about it is to go to a couple of other verses which show who the Word has to have been.
Isa 44:24 Thus says the Lord, your Redeemer,
who formed you from the womb:
“I am the Lord, who made all things,
who alone stretched out the heavens,
who spread out the earth by myself, (See also Job 9:8)
Psalm 102:25 In the beginning you laid the foundations of the earth,
and the heavens are the work of your hands.
We can see in these verses that God alone stretched out the heavens and that the heavens are the work of God's hands. Nobody else was there, God alone did it.
Then we see at Heb 1:10 that these things are attributed to Jesus.
God was alone doing it, Jesus was there doing it. What is the logical conclusion?
Heb 1:10 “In the beginning, Lord, you laid the foundations of the earth,
and the heavens are the work of your hands.
Interestingly this is one of those places where "Lord" should probably have been translated as "Jehovah" in the NWT since Psalm 102 is speaking of God. But that is another topic.
Anyway we now can see that the Word, since He was God at the beginning, did not have a beginning.
Since John 1:1-3 is speaking about the Word (prehuman Jesus) and His origins and who He is, I don't expect it to say anything about the Holy Spirit. Nevertheless I bet you agree with me that God's Holy Spirit was there. Just who/what the Holy Spirit is can be seen in other passages.