Then Peter stood up with the Eleven, raised his voice, and proclaimed: "You who are Jews, indeed all of you staying in Jerusalem. Let this be known to you, and listen to my words. You who are Israelites, hear these words. Jesus the Nazarene was a man commended to you by God with mighty deeds, wonders, and signs, which God worked through him in your midst, as you yourselves know. This man, delivered up by the set plan and foreknowledge of God, you killed, using lawless men to crucify him. But God raised him up, releasing him from the throes of death, because it was impossible for him to be held by it. For David says of him: I saw the Lord ever before me, with him at my right hand I shall not be disturbed. Therefore my heart has been glad and my tongue has exulted; my flesh, too, will dwell in hope, because you will not abandon my soul to the netherworld, nor will you suffer your holy one to see corruption. You have made known to me the paths of life; you will fill me with joy in your presence. "My brothers, one can confidently say to you about the patriarch David that he died and was buried, and his tomb is in our midst to this day. But since he was a prophet and knew that God had sworn an oath to him that he would set one of his descendants upon his throne, he foresaw and spoke of the resurrection of the Christ, that neither was he abandoned to the netherworld nor did his flesh see corruption. God raised this Jesus; of this we are all witnesses. Exalted at the right hand of God, he received the promise of the Holy Spirit from the Father and poured him forth, as you see and hear."
Acts is written by Luke who was not an eyewitness to the Life, Death, and Resurrection of Jesus. He is a convert and writing from the oral tradition handed down by the Apostles. This is why he assures the crowd that they are hearing the Truth, passed down from Peter and the Apostles. To reassure the people even more, Luke shows that Jesus fulfills David's prophecy.
We believe and we, like Luke, weren't there with Jesus. We have scriptures, traditions, and magisterium to aid our faith. We trust in Jesus.
O my God, I believe You are always there. I believe You sent Your Son, Jesus, to make up for Adam and Eve's sin. I believe Your inspired Word. I also believe in the Holy Catholic Church, which Jesus founded. This is my faith.