Few people know this, but I was baptized twice, once as an infant in a Presbyterian church and again 11 years later in a Baptist church. Much later again, after returning to my Reformed roots, I came to see my "second baptism" as a reaffirmation of my earlier baptism. Here is Hughes Oliphant Old on baptism:
Baptism when it is administered to children is a particularly clear sign that God out of his grace has taken the initiative for our salvation. If the classical Reformers of sixteenth-century Protestantism continued the practice of administering baptism to infants, it was because they had a very strong theology of grace. While the Reformers were strongly Augustinian, their opponents were openly Pelagian! The Anabaptists believed in decisional regeneration. That is, they believed one is saved by making a decision for Christ. There is a big difference between decisional regeneration and justification by faith. While the baptism of infants was perfectly consistent with a strong doctrine of grace and with the doctrine of justification by faith, it was not consistent with any kind of theology that makes salvation a matter of human decisions (Worship Reformed according to Scripture, p. 19).
While Old might have put the matter a bit less provocatively, I believe he is fundamentally correct to tie baptism to God's grace rather than to our own decision. I myself have always been conscious of belonging to Christ. To be sure, I have had moments of heightened sensitivity to my own sins and to the need for conversion. But these did not and could not save me. God's grace did that.