Paul NEVER said that the true God is "not the Son".
You are ASSUMING a "mutual exclusion" that God must be EITHER the Father OR the Son, but not both, and Paul NEVER teaches that.
Quite the contrary, Paul explicitly refers to:
"the Christ, who is God over all,
blessed forever." (Rom. 9:5)
"our great God and Savior
Jesus Christ" (Tit. 2:13)
You are ASSUMING unitarianism, "only one person per God".
Actually, YOU are the one "ignoring what ELSE Paul said".
YOU are ignoring where he said, "There is NO GOD ELSE but ONE."
Now, you are either unaware of alternative interpretations of your proof-text, or else you are pretending there aren't any, since your false theology requires you to ignore them.
FIRST Paul says, "there is NO GOD ELSE but ONE."
That is simply a statement of fact.
Only one God. Period.
Then He says, 'to us there is but on God".
Now we have to ask ourselves, is he saying that because there are other gods who actually exist (denied throughout the Bible), but they simply aren't relevant "to us"?
Or is he saying that because there is only one God "to us", because "we" recognize only one true god exists, and all the others are false gods and idols? I think it's the latter.
There is also a larger aspect of Paul's teaching that you are missing.
Paul was a devout Jew, and prayed the Sh'ma, every single day:
Deut. 6:4 “Hear, O Israel: The LORD
our God, the LORD
Deut. 6:4 “Hear, O Israel: The <YHWH> our God, the <YHWH> is one.
This is the Jewish prayer/proclamation that YHWH was the only god who exists.
He is both "God" and "Lord". "God" is WHAT He is ("elohim" = "a god"), and "YHWH" is WHO He is (His name, YHWH, Yahweh, or Jehovah).
So what Paul is doing in 1 Cor. 8:6 is giving an EXPANSION of the Sh'ma, which teaches only one god exists, and including BOTH the Father and the Son as that one True God:
|Deut. 6||1 Cor. 8|
|Hear, O Israel:|
the LORD is one.
|yet for us there is|
one God, the Father, from whom are all things and for whom we exist,
and one Lord, Jesus Christ, through whom are all things and through whom we exist.
Both are God.
Both are LORD (which is the name of God).
But for convention, to distinguish between them, Paul generally refers to the Father as "God" (which does not deny that He is also Lord), and generally refers to the Son as "Lord" (which does not deny that He is also God).
It is irrational to take a passage where Paul includes both the Father and the Son as the one true God of Israel, and misrepresent that as Paul allegedly claiming that they are two gods, or that Jesus isn't God.
"Father" and "Son" refer to WHO they are.
"God" refers to WHAT they are.
Jesus is Deity.
The Father is Deity.
There is only one Deity.
Deity is not a "person".
Deity is "what" they are.