Justification means to be considered righteous. Paul discusses “the righteousness of God, which is by faith of Jesus Christ unto all and upon all them that believe” in Rom 3:22; see also Phil 3:9. Those who are considered righteous (i.e. justified) are those who believe, and it is by faith. “Abraham believed God, and this was accounted to him for righteousness” (Gal 3:6, see also Gen 15:6) – again, believers are accounted as righteous (i.e. justified). “All that believe are justified” (Acts 13:39). In Ro 5:1 and Gal 3:24, Paul says we are “justified by faith”. In 1 Cor 6:11, Paul says “ye are justified in the name of the Lord Jesus by the Spirit of God” – this is addressed to the church (see 1 Cor 1:2), i.e. believers.
Through His death on the cross, Jesus has justified us and made us righteous (Rom 3:22-24, 4:6, 5:9, 6:18, Gal 2:16). The book of Titus is a wonderful letter, in which Paul discusses how we are justified by the grace and mercy of God (2:11, 3:4, 7), the sacrifice of Christ (2:14).
Romans 5:1 says “being justified by faith, we….” So this verse says “we” i.e. those Paul was writing to, believers, and it also says that we are justified by faith.
Rom 5:18, which in its context means that justification is offered to all, not that all are justified, as is indicated in verse 19 which says “shall many be made righteous” – so many, not all are righteous.
Gal 2:16, says that we are justified by the faith of Christ.
In Rom 8:29-30 again those whom God foreknew, predestined to be conformed to the image of Jesus and called, he justified and glorified.
In Rom 3:23-24 Paul says “all… being justified freely”, he does not say all are justified. In verse 26, just two verses after this, Paul says Jesus is the justifier of those who believe in Jesus.
Note that Believers, or those who have faith, are justified; unbelievers are not justified until they believe.
We were sinners but now we are washed, sanctified and justified (1 Cor 6:11).