It was prophesied well in advance that the gospel would go to the Gentiles as well:
Romans 15:8-12
8Now I say that Jesus Christ was a minister of the circumcision for the truth of God, to confirm the promises
made unto the fathers:
9And that the Gentiles might glorify God for
his mercy; as it is written, For this cause I will confess to thee among the Gentiles, and sing unto thy name.
(2 Samuel 22:50, Psalm 18:49)
10And again he saith, Rejoice, ye Gentiles, with his people.
(Deuteronomy 32:43)
11And again, Praise the Lord, all ye Gentiles; and laud him, all ye people.
(Psalm 117:1)
12And again, Esaias saith, There shall be a root of Jesse, and he that shall rise to reign over the Gentiles; in him shall the Gentiles trust.
(Isaiah 11:10)
The "transition" that you are saying is in Acts just doesn't exist. Acts 2:38 addresses Jews because those were the people who were literally present at that moment. Had Gentiles been present they would have addressed them as well.
Eventually, once they got out of Jerusalem and moved on, they did go to the Gentiles and told them to repent, be baptized, and believe the Gospel of Christ just like Acts 2 says for the Jews.
1. Repent (2 Corinthians 7:10)
2. Be baptized (1 Corinthians 1:14-17)
3. They believed (1 Corinthians 15:1-4)