I would be one of those to whom your question is addressed, but you seem to be suffering from something of a misunderstanding about this stance, which you think needs to be reconciled with the Bible.
First, there is no "only" about Christian baptism. It's not 'only' a ceremony, or 'only' a confession of faith, nor is it 'only' an optional extra. Further, it shows the grace of God towards a person being baptised biblically, so this is where you might need to do a double-take on what the grace of God involves and incorporates.
Start with Noah, as you specifically asked that verse about him to be reconciled with the view that those such as I have.
The whole object of the exercise of the flood-waters and the ark was to keep Noah & Co. from getting even a drop of water on them. The ark symbolised a gracious means of God saving some. Noah and his family were never literally baptised in water. But spiritually, or symbolically, they passed through the flood-waters and came out alive. So with Christian baptism, the person goes into the waters and comes out not only alive, but his or her going in symbolises a spiritually dead person being raised to newness of spiritual life. It is a miracle of grace on a par with the flood and the ark, and is the Christian symbol of having been saved by his grace.
I was going to detail more but note that Nigel J. has succinctly covered the essential points, showing the immensity of what baptism is, and of God's gracious provision. I would only add that your quotation of 1 Peter 3:21 stopped short of the essential point that proves the point of what saves a person : the resurrection of Jesus Christ, which the person puts faith in and thereby obtains a good conscience toward God. Anybody seeking biblical baptism without first having put faith in Christ and his resurrection is not a fit candidate for it. Here is some explanation from a Reformed Presbyterian source:
"1. Baptism is a sacrament of the New Testament, ordained by Jesus
Christ, not only for the solemn admission of the party baptized into
the visible church, but also to be unto him a sign and seal of the
covenant of grace, of his ingrafting into Christ, of regeneration, of
remission of sins, and of his giving up unto God through Jesus Christ,
to walk in newness of life: which sacrament is, by Christ's own
appointment, to be continued in his church until the end of the world.
- The outward element to be used in this sacrament is water, wherewith the party is to be baptized in the name of the Father, and
of the Son, and of the Holy Ghost, by a minister of the gospel,
lawfully called thereunto." (The Westminster Confession of Faith for
Study Classes, G.I. Williamson, p207)
When the word 'sacrament' is applied to baptism, as it is above, it is taken to mean:
A "...holy sign and seal of the covenant of grace, immediately
instituted by God, to represent Christ and his benefits, and to
confirm our interest in him; as also to put a visible difference
between those that belong unto the church and the rest of the world;
and solemnly to engage them to the service of God in Christ, according
to his word." (Ibid. p 200)
There could be no salvation of God, in Christ, without God and Christ graciously acting first. There could be no Christian baptism without God and Christ having graciously acted first. Whatever anybody believes about Christian baptism, I trust we can all agree that it is all of God, and must always be to his glory, and not a sort of spiritual football to kick around a pitch, supporters on either sides egging their 'team' on.