The Scripture is clear that God saves. Jonah 2:9 tells us that "Salvation is from the Lord". Zephaniah 3:17 encourages us with the reality that "God is mighty to save". As God accomplishes our salvation, we see all three members of the Trinity at work: God the Father, God the Son, and God the Spirit.
We see this in Ephesians 1:3-14, where we read:
3 Praise be to the God and Father of our Lord Jesus Christ, who has blessed us in the heavenly realms with every spiritual blessing in Christ. 4 For he chose us in him before the creation of the world to be holy and blameless in his sight. In love5 he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will– 6 to the praise of his glorious grace, which he has freely given us in the One he loves. 7 In him we have redemption through his blood, the forgiveness of sins, in accordance with the riches of God's grace 8 that he lavished on us with all wisdom and understanding. 9 And he made known to us the mystery of his will according to his good pleasure, which he purposed in Christ, 10 to be put into effect when the times will have reached their fulfillment–to bring all things in heaven and on earth together under one head, even Christ. 11 In him we were also chosen, having been predestined according to the plan of him who works out everything in conformity with the purpose of his will,12 in order that we, who were the first to hope in Christ, might be for the praise of his glory. 13 And you also were included in Christ when you heard the word of truth, the gospel of your salvation. Having believed, you were marked in him with a seal, the promised Holy Spirit, 14 who is a deposit guaranteeing our inheritance until the redemption of those who are God's possession–to the praise of his glory.
Regarding our salvation, God saves. Here is a quick take on how the Trinity works together to save:
The Father thought it. This is the providence of the Father.
The Son bought it. This is the propitiation of the Son.
The Spirit wrought it. This is the power of the Spirit.
