let’s look for the “symbol” in either verse:
acts 2:38 “and peter said to them “repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of sins and you will receive the gift of the Holy Spirit”
clearly no symbol there, let’s see what Acts 22 say:
Acts 22:16 “and now why do you wait? Rise and be baptized, and wash away your sins, calling on his name”
again, no symbol.
maybe your Bible contains the word symbolic in these passages, if so, please tell me what version you use!!
Acts 16:31 Paul and silas say to the jailor, "Believe in the Lord Jesus and you will be saved..." They were baptized after, but here it is belief which is spoken of as saving them.
Paul often talks of belief as sufficient for righteousness. I will give you one example. "Abraham believed God and it was credited to him as righteousness." Obviously Abraham was not baptized.
I'ts not a pie-in-the-sky "lone ranger" interpretation to believe that baptism doesn't CAUSE regeneration but is an outward proof. It is believed by many based on Scripture.