The cross made salvation possible for all. Our faith makes it actual for the individual.
1Jn 2:2 He Himself is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world.
but it is only those that have trusted in the risen Christ that will be justified/saved.
Rom 4:5 However, to the one who does not work, but believes in Him who justifies the wicked, his faith is credited as righteousness.
Joh 1:12 But to all who did receive Him, to those who believed in His name, He gave the right to become children of God
Our justification is grounded in Christ Jesus but we are justified because we believe.
Rom 5:1 Therefore, since we have been justified through faith, we have peace with God through our Lord Jesus Christ,
Rom 5:2 through whom we have gained access by faith into this grace in which we stand. And we rejoice in the hope of the glory of God.
In the NT we find six aspects of Justification
We are justified by grace (Tit_3:5-7, Eph 2:8-9) — that means we do not deserve it.
We are justified by faith (Rom_5:1-2, Gal 2:16) — that means that we have to believe on the Lord Jesus Christ to receive it.
We are justified by blood (Rom_5:9-10, Rom_3:25) — that refers to the price the Savior paid in order that we might be justified.
We are justified by power (Rom_4:24-25) — the same power that raised the Lord Jesus from the dead.
We are justified by God (Gal_3:8-9, Rom 3:30) — He is the One who reckons us righteous.
We are justified by our works (Jas_2:18, Jas_2:24, Jas 2:26) — not meaning that good works earn justification, but that they are the evidence that we have been justified.