In the last sentence, your conclusion doesn't follow. By definition, if Jesus is eternal, then he cannot be a part of creation, since creation began at a point in time.
Context is king; it is what determines meaning. So, let's look at the context:
Col 1:15 He is the image of the invisible God, the firstborn of all creation.
Col 1:16 For
by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—
all things were created through him and for him.
Col 1:17 And
he is before all things, and in him all things hold together.
Col 1:18 And he is the head of the body, the church. He is the beginning, the firstborn from the dead, that in everything he might be preeminent. (ESV)
If, as you claim, "the firstborn of all creation" means that "Jesus is a created being," then Paul immediately contradicts that with verses 16 and 17. The logic is very simple: if
all things were created by Jesus, then Jesus
cannot be created. Put the other way: if Jesus was created, then it necessarily cannot be the case that everything was created "by" and "through" him. That is, if even one thing was created without the Son, such was the Son himself, then it is logically impossible that "all things" were created by him. There is no other logical conclusion.
So, where does that leave us with verse 15? It means there must be another meaning of "firstborn," and it is hinted at in verse 18--"that in everything he might be preeminent" (see also Rev 1:5). And we can see from other places in Scripture that "firstborn" certainly means exactly that--preeminence or sovereignty:
Exo 4:22 Then you shall say to Pharaoh, 'Thus says the LORD, Israel is my firstborn son, (ESV)
Psa 89:20 I have found David, my servant; with my holy oil I have anointed him,
...
Psa 89:27 And I will make him the firstborn, the highest of the kings of the earth. (ESV)
Jer 31:9 With weeping they shall come, and with pleas for mercy I will lead them back, I will make them walk by brooks of water, in a straight path in which they shall not stumble, for I am a father to Israel, and Ephraim is my firstborn. (ESV)
We see then that "firstborn" has meanings which are not literal. We know from reading the Bible that the firstborn had certain rights and privileges but we also see in the verses above that it seemed those whom God loved, those with whom he had relationship, he called his firstborn, even though they were not in any literal sense his firstborn.
The use of firstborn can mean preeminence without the referent having actually been born. Looking at the significance of
Psalms 89:27, it is a messianic Psalm where God says of David, "I will make him the firstborn." Here, firstborn clearly means that God will put him in a position of preeminence, "the highest of the kings of the earth." David is here the prototype of the coming Messiah, the "firstborn," and has nothing to do with David's being born or coming into being. This is almost certainly what Paul had in mind, and we see something similar in Romans:
Rom 8:29 For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. (ESV)
Here is means the same--that Jesus would be the head of all believers.
In relation to the Son then, we can understand that
Col. 1:15 is speaking of Jesus's place of pre-eminence, his sovereignty, and his lordship, over all creation.
As an aside, one can easily see that Col 1:16-17 agree with John 1:3: "All things were made through him, and without him was not any thing made that was made." The logic is, again, inescapable. If all things were made through the Son, then the Son cannot be made.
As I have shown, and can continue with many other verses, the Son has no beginning, he is eternal. That is precisely why Trinitarians are correct to say that he is of the same essence or substance of the Father, why he is truly and fully God just as the Father is truly and fully God.
You say that a '"son" has a beginning.' In human terms, yes, that is correct, but why? It is because we are of the same substance as our parents. The Son of God, if he is in any true sense God's Son, must then necessarily be of the same substance as the Father, correct? That means that the substance of the Father is eternal and, therefore, the substance of the Son is eternal. Again, it can only mean the Son has always existed. Again, this was a claim to deity, for which, as we have already seen, the Jews tried to kill Jesus.
Be careful when arguing to the use of "begotten." There are not only multiple Greek words translated as "begotten," with different meanings, it may be used literally or figuaratively.