Jesus did not give that option to the Apostles: "And Jesus coming, spoke to them, saying: All power is given to me in heaven and in earth. Going therefore, teach ye all nations; baptizing them in the name of the Father, and of the Son, and of the Holy Ghost. Teaching them to observe all things whatsoever I have commanded you: and behold I am with you all days, even to the consummation of the world." (Matthew 28:18-20)
He commanded His disciples to teach and to baptize.
And what were some of Jesus's teachings?
John 3:5 provides one: "Amen, amen I say to thee, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God."
But the most telling thing comes from verse 33 of Acts 16: "And he, taking them the same hour of the night, washed their stripes, and himself was baptized, and all his house immediately."
Baptism is central to Christian belief; I don't know how anyone can rightly say otherwise.
Ah, but “even the demons believe and tremble;” clearly belief is not sufficient.
Consider that Christ said, “If you love Me, you will keep my commands,” and elsewhere that the greatest commandment was to “Love the Lord your God with your whole heart, your whole soul, and your whole mind.”
So loving God and keeping His commands enters in as well.
I don’t think we can rest our understanding on something like salvation on just one verse, can we?
Peter was asked the very same question: What must we do to be saved? Acts 2:38 says what?
Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit.
And since baptism is a death, burial and resurrection process, we know that Mr. Thief could not be baptized - not because he was on a cross - but because Jesus had not yet died, been buried and then raised to life. The TOTC was saved by an Old TEstament faith. Like those heroes mentioned in Hebrews 11.
You and I are saved under grace. Which includes baptism. Faith alone won't save you.
Also... You left off a relevant passage in your example of Acts 16. verse 32 and 33.
Then they spoke the word of the Lord to him and to all the others in his house. 33 At that hour of the night the jailer took them and washed their wounds; then immediately he and all his household were baptized.