I noticed you did not highlight Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, and went straight to "unto obedience" to imply we are saved by works.
i Peter 1:1 - 2 Πέτρος (Peter, ) ἀπόστολος Ἰησοῦ Χριστοῦ (an apostle of Jesus Christ, ) ἐκλεκτοῖς παρεπιδήμοις (to elect strangers, dative m. pl.) διασπορᾶς (of/from a diaspora, genitive f. sg.) Πόντου Γαλατίας Καππαδοκίας Ἀσίας καὶ Βιθυνίας (of Pontus, Galatia, Kappadokia, Asia, and Bithynia
κατὰ πρόγνωσιν θεοῦ πατρός (according to Father God's foreknowledge) ἐν ἁγιασμῷ πνεύματος (in/by sanctification of the Spirit) εἰς ὑπακοὴν (into/for obedience, eis + accusative) καὶ (eis) ῥαντισμὸν αἵματος Ἰησοῦ Χριστοῦ (and into/for a sprinkling of the blood of Jesus) χάρις ὑμῖν (grace to you) καὶ εἰρήνη πληθυνθείη (and peace be multiplied).
The word elect is not in the Greek text of verse 2. Some assume the
kata at the beginning of verse 2 is referring to elect strangers being "elect strangers out of a diaspora
according to God's foreknowledge".
Some think the
kata refers to what follows. "Grace to you and peace be multiplied
according to God's foreknowledge... "
Since assuming the first helps your case best, we will do that.
We read that this foreknowledge is
by/in the spirit's sanctification/setting apart for/into obedience, and by/in the spirit's sanctification/setting apart for/into a sprinkling of Jesus' blood.
Foreknowledge is simply knowing or having a relationship beforehand. Peter is simply saying,
" To elect strangers of a diaspora whom God has already come to know
by means of the spirit's setting you apart into obedience and
by means of the spirit setting you apart into sprinkling with Jesus' blood. "
When does the Holy Spirit set us apart into obedience? When we obey and put our trust in Jesus Christ as our Lord and Saviour.
When does the Holy Spirit set us apart into a sprinkling of Jesus' blood? When we put our trust in Jesus Christ as our Lord and Saviour.
When does God start to know us relationally? When we trun to Him with faith in Jesus Christ.
Gal 4:8 Howbeit then,
when ye knew not God, ye did service unto them which by nature are no gods.
Gal 4:9 But now,
after that ye have known God, or rather
are known of God, how turn ye again to the weak and beggarly elements, whereunto ye desire again to be in bondage?
Peter is simply saying that he is addressing elect strangers of a diaspora of Jews in the places listed, and that God already has a relationship with these elect, he has had a relatiuonship with them before now, a relationship which began when they were set apart into obedience and set apart into a sprinkling with Jesus' blood which cleansed them of their sins.