The Shema as found in Deuteronomy is the primary text for "one God:"
“Hear, O Israel: The LORD our God, the LORD is one.[b] (Deuteronomy 6:4) [ESV]
b. Or The LORD our God is one LORD; or The LORD is our God, the LORD is one; or The LORD is our God, the LORD alone
About 200 years before the Christian Era, the Old Testament was translated and so the Shema was rendered into Greek (Septuagint or LXX):
And these are the statutes and the judgments which the Lord commanded to the sons of Israel in the wilderness as they were coming out from the land of Egypt. Hear O, Israel: the Lord our God is one Lord. (LXX NETS)
καὶ ταῦτα τὰ δικαιώματα καὶ τὰ κρίματα ὅσα ἐνετείλατο κύριος τοῗς υἱοῗς Ισραηλ ἐν τῇ ἐρήμῳ ἐξελθόντων αὐτῶν ἐκ γῆς Αἰγύπτου ἄκουε Ισραηλ κύριος ὁ θεὸς ἡμῶν κύριος εἷς ἐστιν
When asked which was the most important commandment, Jesus began with the Shema:
Jesus answered, “The most important is, ‘Hear, O Israel: The Lord our God, the Lord is one.
ἀπεκρίθη ὁ Ἰησοῦς ὅτι πρώτη ἐστίν ἄκουε Ἰσραήλ κύριος ὁ θεὸς ἡμῶν κύριος εἷς ἐστιν [mGNT]
"κύριος ὁ θεὸς ἡμῶν κύριος εἷς ἐστιν," follows the LXX verbatim. Therefore, understanding Paul's use of "one God" should be consistent with the Shema.
Convention From the LXX
The Hebrew for “God” in the Shema is אלהים which is plural and the rendering is not always the singular θεός. However, for a monotheistic Hebrew scholar, wherever אלהים means “God” it would be rendered as singular. This may not always be grammatically correct, but a technically correct translation might fail to accurately communicate the meaning (at least for a Jewish translator).
Consider how the LXX translator(s) handled the first verses of Genesis:
In the beginning, God (אלהים) created the heavens and the earth. The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God (אלהים) was hovering over the face of the waters. (1:1-2)
ἐν ἀρχῇ ἐποίησεν ὁ θεὸς τὸν οὐρανὸν καὶ τὴν γῆν ἡ δὲ γῆ ἦν ἀόρατος καὶ ἀκατασκεύαστος καὶ σκότος ἐπάνω τῆς ἀβύσσου καὶ πνεῦμα θεοῦ ἐπεφέρετο ἐπάνω τοῦ ὕδατος
In the beginning God created the heaven and the earth. But the earth was unsightly and unfurnished, and darkness was over the deep, and the Spirit of God moved over the water.
Where, the meaning is understood as "God" the LXX has the convention of rendering אלהים as ὁ θεὸς, the God. So, "In the beginning the God created the heaven and the earth." Since the concept of capitalization did not yet exist, the definite article was used to demonstrate what in English is "God." Obviously, in the Greek world, θεὸς does not necessarily convey monotheism. Zeus was θεὸς. However, the LXX translator(s) would argue Zeus was not ὁ θεὸς.
The next verse deviates from the convention. "God" is the same "God" as in verse 1; yet it is written without the definite article. So for the person who would understand "Spirit of God" from the position of the Trinity, they see when writing about a singular aspect of the Trinity, "God" was written without the definite article.
Then a general convention derived from the LXX is "God" as in the Godhead was written with a definite article and "God" when used in conjunction with the Spirit (or Father or Son) would be written without the definite article.
Paul's Different Uses
one God and Father of all, who is over all and through all and in all. (Ephesians 4:6)
εἷς θεὸς καὶ πατὴρ πάντων ὁ ἐπὶ πάντων καὶ διὰ πάντων καὶ ἐν πᾶσιν
For there is one God, and there is one mediator between God and men, the man Christ Jesus,
(1 Timothy 2:5)
εἷς γὰρ θεός εἷς καὶ μεσίτης θεοῦ καὶ ἀνθρώπων ἄνθρωπος Χριστὸς Ἰησοῦς
since God is one—who will justify the circumcised by faith and the uncircumcised through faith.
εἴπερ εἷς ὁ θεός ὃς δικαιώσει περιτομὴν ἐκ πίστεως καὶ ἀκροβυστίαν διὰ τῆς πίστεως
The English translations obscure what is obvious in the Greek: Paul only uses the definite article in Romans indicating he is following the LXX pattern from Genesis. The purposeful omission of the definite article indicates the reader is to understand there is a difference between ὁ θεός and simply θεός. In fact, as writing at that time did not include spaces between words, it is possible ὁ θεός was pronounced “ὁθεός.”
Regardless, it is clear from Paul’s varied uses, “one Father” is not ὁ θεός and the only reason for ignoring the distinction in the texts is the theological position “One Father” is “The God.” On the other hand, Paul’s omission of the definite article when used with "Father" is consistent with the LXX translator(s) treatment of "Spirit" in Genesis 1:2.
When Paul wrote "one God" in a passage which spoke of Father, he omitted the definite article, showing "Father" is not ὁ θεὸς. When he wrote "one God" in the passage in which there was no separate mention of the Spirit and Son, he included the definite article. Thus, Paul is following a Trinitarian's understanding of the LXX Genesis.
As Paul made a clear distinction in both the letter to the Ephesians and to Timothy (who was at Ephesus at the time), there is no linguistic support to consider those passages equivalent to the one in Romans or the Shema. Rather, by omitting the definite article he was following the LXX which omitted the definite article when writing about a singular aspect of the Trinity.