Galatians 3:28-29
There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
First, the New Covenant writings from Matthew to Revelation are written by Jewish Christians (Luke, Matthew, Saul, Peter, James, etc.), to and for Jews and other Jewish Christians and your quote of Galatians 3:28-29 is referring to those under the Law or "schoolmaster", and those under the Law/schoolmaster are the children of Israel, not Gentiles. God made no covenant with Gentiles. None.
Notice Saul says "Greek" and not "Gentile."
The "Greek" he is referring to are Hellenized Jews who grew up in Gentile lands heavily influenced by Greek culture. Even to the point of Jews not ever been circumcised because these Jews grew up as Gentiles in Gentile lands. They lost their Hebrew heritage and for 15-20 generations from 522 BC to when Jesus arrived knew nothing about Him. Jesus never left Israel/Palestine. He may have gone into Galilee and Decapolis but that's the extent of His travels. When Jesus was crucified the only people who knew live in Jerusalem or they were Jews who traveled from Gentile locations for the Jewish Feast of Harvest. One of three Feasts God mandated males attend and observe.
5 And there were dwelling at Jerusalem Jews, devout men, out of every nation under heaven. Acts 2:5.
7 And they were all amazed and marvelled, saying one to another, Behold, are not all these which speak Galilaeans? 8 And how hear we every man in our own tongue, wherein we were born?
9 Parthians, and Medes, and Elamites, and the dwellers in Mesopotamia, and in Judaea, and Cappadocia, in Pontus, and Asia,
10 Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes,
11 Cretes and Arabians, we do hear them speak in our tongues the wonderful works of God.
Acts 2:7–11.
Take note that the prophet Joel prophesied and said God promised His Spirit TO ISRAEL, not to Gentiles. So this means that three thousand Jews were given the Holy Spirit as promised by God and they and ONLY they were the first recipients of this promise from God. And when the Feast was over these Spirit-filled Jews left Jerusalem and traveled back to their homes in and around Israel and also Asia Minor or Gentile land (Roman provinces), taking with them a summary of Peter's sermon, the Holy Spirit and a testimony of Jesus and what they experienced. It was a powerful witness of God these born-again Jews gave along in their travels.
There is nowhere in the Bible that says God ever promised His Spirit to Gentiles. Nowhere.