Peter is writing his letter to resident aliens and migrant workers in Asia Minor, and they want to know how to live in the Roman Empire. Why do they ask such a question? Because they are now living in the way of Jesus. What difference does that make?
Here’s how Peter says it. I give my own translation of 1 Peter 1:1-2: “Peter, the Apostle of Jesus Christ, to the chosen temporary residents in the diaspora of Pontus, Galatia, Cappadocia, Asia, and Bithynia — those who are chosen by God according to Father God’s foreknowledge by the Spirit who makes us holy — and who makes us holy so we will be obedient — and who chooses us by sprinking Jesus’ blood on us. Grace to you and may peace [shalom] be multiplied on you.”

Peter’s resident aliens and migrant workers, in spite of their social class, have been redeemed by the work of the Father God (of Jesus). Redemption — here in the terms of being made holy and through Jesus’ death — is designed to create obedient folk.
Notice the trinitarian nature here: Father’s foreknowledge, Spirit’s making holy, and Son’s death.
They may be resident aliens and temporary residents, but they’ve been encircled by the ambit of the Trinity:
1. the Father knows them and makes them his;
2. the Spirit is making them holy;
3. the Son has forgiven them.
There is the foundation of knowing how to live as resident aliens and temporary residents in the Roman Empire: know who you are and whose you are and how you got there. Most of all, know what God is up to in this world and get involved.
It would be a mistake to think Peter is thinking individualism here. Peter has the big picture in mind: the Father, Spirit, and Son at work is the redemptive work of God in this world, and not just the redemptive work for individuals so they will become holy and consecrated. So they can get saved “from” the world. In fact, the resident aliens and temporary workers want to know how to make a missional impact on the world around them and have asked Peter how they are to do that. Peter says the answer begins with knowing what God is doing in the world. Making folks holy and forgiving sins and drawing them to himself.
Just why Peter grounds his letter in this trinitarian work of God is not clear yet, but it has to do with the rest of the letter: and that letter focuses on how to live in this world in such a way that God’s redemptive work is given full sway.
My suggestion is that Peter’s (early) trinitarian theology is the beginnings of recognizing the contribution of each to the whole, of the “community Who is God,” and this shapes his entire community apologetic: his intent is to form a community that provides an alternative to the secular-shaped power-mongering of Caesar.