Who is Peter speaking to in the early chapters of Acts?
In the early chapters of Acts, Peter is speaking to the nation of Israel, not to the Church or to Gentiles. He and the other eleven operate solely on the Old Testament program, giving Israel opportunity to repent of rejecting their Messiah and the offered Kingdom.
Les explains that as you go through the early part of Acts, Peter and the other eleven apostles operate only on what God has revealed—the Old Testament program. Peter has no concept of God turning to the Gentiles for 1900 and some years. God is giving Israel every opportunity to yet repent of what they had done to their Messiah. So Peter isn't talking to the church, and he's not talking to Gentiles; he is addressing Israel. Les also notes that the Church and rapture are not found in the Gospels or Old Testament because they are a secret held in the mind of God. After Christ ascended, Israel kept rejecting the offer of the King and the Kingdom, so God moved that program into the future and inserted an undetermined period of time before the seven years and Christ's return.