Do you believe that the preached word is "necessary – that no one may omit it from either neglect or contempt," as pertains to our salvation?
As a matter of predication, God does his saving work all by himself, without any external inputs. The Holy Spirit acts in regeneration and all his work by his own creative and restorative supernatural power, not leveraging man's inputs or anything in creation to arrive at his ends. These things are true, at the same time that God has purposed and ordained that he will work by certain means unto saving ends; which particulars he explains in his word so that we who receive that word should be aided and strengthened in our faith.
So we accept that, had he intended he might have simply worked savingly in the heart of this one or that without the association of any means; but he preferred the use of means, specifically his word mediated through a less-than-perfect instrument. In this way, Calvin or you or I might well say that the preached word is "necessary" for salvation--not absolutely, but without a doubt providentially.
One way the word is represented to and received by believers is through those two, dominical sacraments he appointed. They alone are the authorized means of visibly, tactilely, olfactorly, and lingually (i.e. the senses other than hearing) signifying to men the truth and benefits of the gospel. God works by the use of means. Ergo, baptism is "necessary – that no one may omit it from either neglect or contempt." It is not the Reformed view (following Calvin) that the sacraments themselves or their use create or initiate faith, but liven and strengthen faith. To omit by neglect or contempt would be the opposite of faith, even if it was dressed up in the terms of piety--as when some say, "I don't trust in human activity, as I am more spiritually minded than that." Instead, faith makes due use of the ordinary means God has appointed, putting faith not in the means themselves but in the God of the means.
Did baptism regenerate the adult convert who submitted him to the church's baptism following his profession of new faith? Should we read Calvin to say that regeneration of his soul must have waited on his formal union with the body of Christ on earth? Surely not. Yet, baptism is necessary for God has willed it. It did not create faith where none existed before, or add some sufficiency to weak, self-produced faith; but it was (one may say) a kind of first-watering of the seed of faith that had sprouted within him by the will, work, and word of God. It supplied an indescribably important and vital benefit at a crucial moment.
What of the infant, who lacks the intellectual maturity to grasp the word in its standard mode of verbal expression? How is baptism necessary to him, if it does not create faith or a state of grace at the moment of its application? Or as it does not (cannot) at that time act on faith's tiny sprout? Some of the early reformers actually conceived that the "seed of faith" in the elect was watered by infant baptism in order to sprout it. It seems, over the years and centuries, the Reformed have moved away from that concrete concept of faith as a seed-sprout-plant within (could we find it still at its smallest, if we searched the correct room of the heart?) to a faculty of the soul that is either quick or dead.
One result of dropping the earlier concept (as a utilitarian analogy, it's neither bad nor good): a certain perspective on baptism's benefit to an elect infant was lost (perhaps for a better gain). Yet, we shouldn't abandon the idea that this child derives benefit from baptism. Baptism is when God early speaks to him more through the caress of water upon his skin than the meaning of the murmuring of the words of institution. Later on, when he is able to apprehend the meaning of that sign (much as he is able to appreciate his physical birth only long after the occasion), that God so spoke early to him ought to make the professor that much more aware of God's singular care and providence toward him his whole life, even before he had any awareness or could admit God's saving communication cognitively.
God made baptism necessary for him, and saw to it that the sign was delivered to him very early; whereas he grew into realization of its necessity and benefits as opposed to adopting a convert's perspective. He became aware that there is a sacramental union between the sign and the thing signified. He looked at the sign (an existing thing) as it was given (once upon a time) and now sees in it God's washing and renewing instrument. Thus, he who is baptized as a child or an adult finds the efficacy of baptism is made unto faith. The efficacy is not tied to the moment of administration. Perhaps, if it is the will of God, his supernatural regeneration could begin at birth, or at his baptism, or previous to either as it was for John the Baptist in the womb; or that supernatural efficacy could be delayed for one reason or another for a course of many years and dark wanderings.
Still for the elect, the day of new life must come before this life comes to an end. The promise of God embedded in baptism is made sure by the exercise of saving faith, by the spiritual apprehension of Christ in his saving glory. We may say the communication from God through baptism--which is a saving word and necessary--has its moment in time; and there is the moment of reception of that word by a heart regenerated, made capable (faculty quickened) of accepting that communication for all its worth.
I hope this is helpful and maybe clarifying.
