Peter’s response is more pastoral than argumentative. There are no fancy theologically-loaded words. He doesn’t argue Scripture with them. He doesn’t argue with their underlying beliefs. Verse four says that Peter “explained…step by step” his experience of God’s work among the Gentiles. Peter appeals to his experience of God and of the Gentiles’ reception of the Spirit. He basically says, “Let me tell you a story…”
In Acts the public sharing of personal experiences of God is a vital part of the ongoing sharing of the good news.