Peter's hearers in Acts 2 were lost/unrighteous. They heard Peter preach the gospel and believed (faith comes by hearing Rom 10:17) and asked what shall we do.
They were commanded to repent and be baptized for the remission of sins. They were was still lost/unrighteous when they believed. Still lost/unrighteous when they repented. Still lost/unrighteous until after they were baptized.
Acts 3:19 - 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. *What happened to baptism?
Acts 10:43 - To Him all the prophets witness that, through His name, whoever believes in Him will receive remission of sins. 44While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. 45 And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit (compare with Acts 2:38 - the gift of the Holy Spirit) had been poured out on the Gentiles also. 46 For they heard them speak with tongues and magnify God. 47 Then Peter answered, "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?" *What happened to baptism in verse 43?
Acts 11:17 - If therefore God gave them the same gift as He gave us when we were baptized? NO when we first kept all of His statutes and did what was right? NO - when we believed on the Lord Jesus Christ, (Acts 16:31 - Believe on the Lord Jesus Christ and you will be saved) who was I that I could withstand God?" When they heard these things they became silent; and they glorified God, saying, "Then God has also granted to the Gentiles repentance unto life. *What happened to baptism?
Acts 15:8,9 - So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us, and made no distinction between us and them, purifying their hearts by faith. *What happened to baptism?
Eze 18:27 "Again, when the wicked man turneth away from his wickedness that he hath committed, and doeth that which is lawful and right, he shall save his soul alive."
The question I asked is how can a man save his own soul? You did not answer that but just asked me more questions. He saves his own soul by doing GOD's righteousness.
As Peter told his listeners to save yourselves by obeying God in repenting and being baptized. Doing nothing/faith only saves no one.
Eph 2:8 "Not of works" refer to works of merit and does not refer to doing God's obedience.
Just saw from Ezekiel the wicked must FIRST do what is lawful and right THEN he saves his soul alive. Cannot eve be saved without doing GOD'S righteousness.