Peter is not stating that Jesus is the LORD (God), but he quotes and expounds Psalm 110:1 where The LORD (Yahweh), that is God the Father is distinguished from David’s Lord (Adon), that is our Lord Jesus Christ, the Son of God.
Dr. Stanley D. Toussaint, Senior Professor Emeritus of Bible Exposition at Dallas Theological Seminary, writes the following commentary on Acts 2:36:
"Here is the conclusion to Peter's sermon. The noun 'Lord', referring to 'Christ', probably is a reference to Yahweh. The same word 'kyrios' is used of 'God' in verses 21, 34, and 39 (cf. Phil. 2:9). This is a strong affirmation of Christ's deity" (The Bible Knowledge Commentary; New Testament, ed. Walvoord & Zuck, [ChariotVictor Publishing, 1983], 359).
Here is a translation of the verse from the
Aramaic Bible in Plain English"
“Let therefore the whole house of Israel know truly, God has made this Yeshua, LORD JEHOVAH and The Messiah, whom you had crucified” (Acts 2:36).
This was still the One Gospel, but after the death and resurrection of Jesus this additional detail was elaborated...
So even though in early acts people were saved by believing a gospel which did not declare that Christ died for our sins that gospel was the same gospel which Paul called "the preaching of the Cross""?
To you the "good news" that Jesus is the Christ, the Son of God, is the same "good news" which declares that Christ died for our sins!
That makes absolutely no sense. Besides that, not long after Paul was converted on the Damascus road he preached the following message to the Jews:
"And straightway he preached Christ in the synagogues, that he is the Son of God.....proving that this is the very Christ" (Acts 9:20,22).
At that time Paul had not yet received the gospel which he was to preach among the Gentiles. He wrote the following:
"But when God, who set me apart from birth and called me by his grace, was pleased to reveal his Son in me so that I might preach him among the Gentiles, I did not consult any man, nor did I go up to Jerusalem to see those who were apostles before I was, but I went immediately into Arabia and later returned to Damascus" (Gal.1:15-17).
When Paul realized on the Damascus road that Jesus is the Christ, the Son of God, he immediately went to Damascus (Acts 9:6-8). But when he received the gospel which he preached among the Gentiles he went immediately into Arabia. That can only mean that two different gospels were preached during the Acts period.