The baptism with the Holy Spirit was foretold of by both John the Baptist and Jesus1,2. Jesus further qualified it as something that would happen to the apostles, giving them power2.
The baptism with the Holy Spirit for the apostles happened just as Jesus said it would2 “not many days” later on the day of Pentecost, which was also the first day the gospel was preached to the Jews in Jerusalem3. That day three thousand were added to Christ.
The second (and only other) time we read of the baptism with the Holy Spirit was at the conversion of the first gentiles4. It was a miraculous (“power”) spectacle just like on the day of Pentecost and was a necessary display to convince Peter, his traveling companions and the Christian Jews back in Jerusalem of God’s acceptance of gentiles into the kingdom4.
It’s evident by these two occurrences in Scripture of the baptism with the Holy Spirit – at the first conversion of Jews and Gentiles (each) – that the baptism with the Holy Spirit was for a specific and special purpose. It was the miraculous ushering in of the gospel “to the Jew first and also the Greek.” (Romans 1:16)