[Cronos]

Note the CONTEXT of Cornelius' baptism -- he was the FIRST GENTILE to be baptised, and this was BECAUSE the Holy Spirit did something unusual -- unlike for Jesus when the Holy Spirit descended at the time of baptism, this was different, this was the Holy Spirit talking to the Apostles telling them to preach and baptise Gentiles without first making them jews

The normal way that happened in every other place in acts and the letters is for the holy Spirit to come in baptism, and then the gifts ofthe Holy Spirit.

However, let me note -- this does not deny the efficacy of baptism, it only points out that baptism is necessary, whether before or after.

[Ruy Dias de Bivar]

I’ll post the verses again.

Act 10:43 To him give all the prophets witness, that through his name whosoever BELIEVETH in him shall receive REMISSION of SINS.

Act 10:44 ¶ While Peter yet spake THESE WORDS, the Holy Ghost fell on all them which heard the word.

Note that after this Peter asked THOSE WITH HIM if they could forbid water. he did not ask God.

[one Lord one faith one baptism]

you have hit the nail on the head, the Holy Spirit was showing Peter the Gospel was for Jew and Gentile alike.
besides, if Ephesians 4 is true and there is only one baptism, and they are claiming the Holy Spirit “baptized” Cornelius, then Peter commanding they be baptized again would make “two” baptisms. no matter how they twist the passages, it doesn’t fit.
besides the clear teaching of Scripture, we have the history of the Church for 1,500 to show what Faith they received from the Apostles, but if they don’t believe the Bible, they won’t be swayed by history.