As a Christian I'm not entirely sure what "salvation of souls" means or looks like. I understand salvation as the salvation of the world.
The biblical language of salvation is rooted firmly in the notion of resurrection. It's not escapism or illumination; but resurrection and restoration.
It is the good Creator God taking the creation, bringing it out from sin, death, etc and renewing it, raising it, restoring it to be the world it is meant to be. This has taken place distinctively in Jesus, who being a man and dying, become the bearer of death in order to render it null and void in His resurrection, whereby in Him humanity itself is raised up, joined to God. What God is going to do for the whole world, He has done in Christ, and Christ is therefore the firstfruits of the resurrection, the beginning of new creation.
In Christian tradition the day Christ rose is called the "eighth day of creation". This is where the symbolism of the number 8 comes from in Christian art and architecture. Baptismal fonts are traditionally octagonal, and many churches have traditionally been built in this way too. A baptismal font being octagonal is symbolic of Baptism's identity with new birth, renewal, and redemption. As in Baptism the individual is taken and joined together with Christ in both His death and resurrection, to be alive by the Spirit, who in us is God's sacred pledge that even as Christ rose from the dead, He will likewise give life to our mortal bodies at the resurrection, at the restoration of all things.
It's why very often Christians will speak saying, "We have been saved, we are being saved, and we will be saved."
We are pointing back to the objective act of Christ's death and resurrection, as well as our individual encounter with and participation in it through our Baptism. That is "We have been saved."
We are pointing to the present reality now, that God is presently saving us, as we hear the Gospel preached, as we confess our sins and hear the Word, "Your sins are forgiven", as we receive the Lord's Supper, Christ's own body and blood for us, to receive Him, and even now, right now, being saved and partaking in the objective reality of God's salvation of the world in Christ and at the end of the age.
We are pointing to the future resurrection of the body, to the Final Judgment, and the renewal of heaven and earth, of all creation, being brought out of death and into the life of God. In Christ. Age to Come, world everlasting.
All of these things are meant by "salvation". A common theme of the New Testament is "now and not yet", that the sacred realities of what God is doing for the world--the resurrection, the restoration of all things, etc--are real and true both at that future day and hour which nobody knows, as well as present now through the active promises of God, through faith. To live into the future reality now, by the abiding of the Spirit living in us, pointing us to what we now presently hope for, having been won for us and made real in Christ's death and resurrection.
It's why the kingdom of God can be said to both be present now and not yet. Present now by these same things, the Christ has come, and He has put death to death in the body, and called the poor and the downtrodden to victory and life in Him. So that even now God's kingdom is present, through the Gospel which declares these things true. And then also at the end of all things, when all will be brought to its fullness.
-CryptoLuthearn