I didn't miss where Paul said we are justified by faith. In fact, I recognize that as a great truth. I do deny that Paul means we become rightous before God by exercising faith in Christ, and it will become apparent in one reads all of Romans.
First of all, justified means declared righteous, not made righteous. Plug that definition in everywhere you see the word in scripture and it will always work out. Made righteous will not.
Secondly, Paul said it is God that justifieth. It is not man that justifieth, but God. Paul also said that to the man who believeth in Him that justifieth the ungodly, his faith is counted for righteousness. God didn't justify the godly, but the ungodly. He calleth those things which be not as though they were. God justified you before you were godly. That word that is translated counted is the greek word logizomai. That word is an accounting term which gives the idea of accounting facts and reality, things that already exist. Paul used that same word in chapter 8 when he said, "I reckon that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us." He's not making something so, but expressing and seeing something which is reality or fact. What Paul is saying is, to the man who trusts in God rather than trying to work his way into righteousness, his faith accounts himself righteous. The righteousness of God is revealed from faith to faith. You were righteous before you placed faith in Christ, your faith is that which sees this fact and applies it to your conscience.
Furthermore, Paul said, "being justified by faith we have peace with God." Didn't say anything about God having peace with us. That's because God doesn't have peace with us through faith. God has peace with us, according to Paul in Colossians, through the blood of His cross. We have peace with God through faith. Being justified by faith is something for us, not God. Paul goes on to say, "by whom (Jesus) also we have access by faith into this grace wherein we stand, and rejoice in hope of the glory of God." Paul said we have access by faith into the grace we are already standing in.
Finally, and the death knell in this argument, we have Paul at the tail end of Romans 4 speaking of Jesus Christ: "who was delivered for our offenses, and was raised again for our justification." Now the word for is the same in english in greek in both parts of that sentence. It must have the same definition in both cases. Why was Christ delivered? Paul said for our offences. He was delivered because of, on account of our offences. He wasn't delivered to gain our offences, but because of them. Thus, we see what the second half of that verse says. He was raised again because of, on account of our justification. He was raised again because we had been justified. That's because we were justified by the death of Christ. Now His resurrection testifies of that fact. Thus Paul says, "who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us."