For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. For in it the righteousness of God is revealed from faith for faith, as it is written, “The righteous shall live by faith.”
The gospel story is the truth to be believed for salvation. It is known by faith, although it is anchored firmly in real historical events. Here is what I mean by "real events": Jesus really existed. No serious scholar questions this. He lived in Roman Palestine. He was a controversial figure. The earliest of Christian creeds acknowledge this historicity of Jesus, even celebrate it, as He "suffered under Pontius Pilate". So you have to deal with Jesus, the very real person.
The very first real claim of the gospel is that Jesus is real. And He caused quite a stir with what He said and did. From the records of His teachings and actions in the gospels, a path clearly points to His redemptive work culminating in dying on the cross and proven by His resurrection from the dead. You have to deal with those parts of the story as well. And it is pretty clear right from the start that again the earliest Christians accepted these facts unquestionably. They gave their lives for them. They believed Jesus died and rose again as Savior from sin and Lord of life.
Paul reiterates here his unashamed commitment to the gospel story. And he does not turn away from faith as being necessary for salvation. We have to believe it. God reveals it "from faith to faith". From start (believing the simple history of it) to finish (accepting the atonement), saving faith is known in Jesus by belief in these truths. Christianity is rooted in faith from facts.