Dr. Michael Bird provides some nice commentary on these opening verses of Romans.
The Apostolic vocation which Paul carries out has as its centrepiece the gospel. Paul was called to be an apostle and set apart for the sake of the “gospel of God”. When Paul mentions the gospel it is most often in association with Jesus Christ as its foci (see 1 Cor 9:12; 15:1-5; 2 Cor 2:12; 4:4; 9:13; 10:14; Phil 1:17; 1 Thess 3:2; 2 Thess 1:8; 2 Tim 2:8). In fact, Paul will very quickly go on to relate the “gospel of God” to the gospel “concerning his son” in 1:3 and the “gospel of his Son” in 1:9 (see Rom 2:16; 16:25). Yet here it is the “gospel of God” (see Rom 15:16; 2 Cor 11:7; 1 Thess 2:8-9; 1 Tim 1:11). The sense is deliberately open as it might mean a gospel from God or a gospel about God. Most likely, both senses are intended. The gospel is both a revelation from God (Gal 1:12) and is about what God himself has done in the faithfulness, death, and resurrection of Jesus the Messiah. To tell the gospel of God is to tell the story of Jesus. And yet the story of Jesus is entirely inexplicable apart from the story of God.
Paul is the quintessential Jesus-freak, but he is not a mono-Jesus adherent. That is because God, Son, and Spirit all figure prominently in his opening narration of the gospel story in Rom 1:1-4. In fact, Romans is the most theocentric letter of the Pauline corpus with the word theos occurring 153 times! John Webster rightly states: “The matter to which Christian theology is commanded to attend, and by which it is directed in all its operations, is the presence of the perfect God as it is announced in the gospel”. As the Apostle sent and set apart by God, Paul sets out before the Roman Christians the story of how God’s plan to repossess the world for himself have now been executed in his own Son, the Lord Jesus Christ.