Peter omits faith here, but includes repentance, baptism, and the Spirit:
Act 2:38 NKJV - (38) Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit.
Peter omits faith, baptism, but includes repentance and what might be interpreted as the Spirit:
Act 3:19 NKJV - (19) "Repent therefore and be converted, that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord,
Peter includes faith, but omits repentance, baptism, and the Spirit:
Act 10:43 NKJV - (43) "To Him all the prophets witness that, through His name, whoever believes in Him will receive remission of sins."
Peter includes baptism, but omits faith, repentance, and Spirit:
1Pe 3:21 NKJV - (21) There is also an antitype which now saves us--baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ,
So, according to the logic that if it is omitted is not necessary for forgiveness, then, what is included commonly in all those passages is the key, right?
Guess what it is common to all of them: nothing. So people don't need to believe, repent, be baptized, or receive the Spirit to be saved, according to Peter.
We can actually do the same with Paul and you will find surprising results.
Better hermeneutics: if it is included
once, it is part of the way to be saved. The reason why it appears in some places but not in others can be explained with linguistics. We all actually practice the same phenomenon, but for whatever reason, some don't expect the biblical writers to do the same?