So, no one brings up the fact that Jesus is God's Son in the first 7 chapters of Acts. Yet this is noticeably absent from the first gospel sermon in Acts 2. Now, I know Acts 2:40 says there were "many other words," and Jesus' sonship is alluded to in Acts 5:31, but no one makes it explicit until the omitted verse of Acts 8:37, or until mentioned explicitly in Acts 9:20. Was it enough for people to know that Jesus was Lord and Christ and crucified for our sins in order to be converted? Is the fact that He is God's Son not a necessary part of our "baptismal cognizance"? I just find it strange. Or was the idea of God having a Son too much for the Jews to accept so soon? -- Fenton Gardner
We know from the Dead Sea Scrolls that “God’s Son” was understood to be the Messiah, so there were definitely Jews around who were comfortable with the concept of the Christ being the Son of God. (Listen to the Dead Sea Scrolls podcast.)
The key thing in baptism is our faith in God through Christ — not the profundity of our theological understanding. Doubtless Jesus taught the apostles on a range of topics in the 40 days following the resurrection, and he may well have amplified his teaching on the nature of the Messiah. Yet all four gospels present Jesus as Son of God, so I think it's unlikely such a foundational teaching would be absent in any early Christian account. Keep in mind that Acts is Luke Part II, and in Luke, Jesus is frequently identified as God's Son (Luke 1:32, 35; 4:3, 9, 41; 8:28; 22:70).
Small note: Acts 8:37 was not an omitted verse, since it was not originally in Acts. It was added in by a later scribe. While it conveys early Christian practice and I don't doubt its veracity, translators did right to remove it once older, better Greek NT manuscripts were discovered. If you are especially fond of the 1611 KJV, you may enjoy my recent podcast on the King James Version