The Abrahamic covenant or promise is central to the Reformed understanding of the unity of the covenant of grace under the Old and New Testaments. We say that there is one covenant of grace with multiple outward administrations. The New Covenant did not first appear in history in the New Covenant. The Old Testament believers were not simply looking forward to the covenant of grace. They were participating in its outward administration in, with, and under types and shadows.
The Southern Baptist Convention (SBC) is the largest evangelical Christian denomination in the USA reporting a total membership of 14.8 million (of whom 1/3 attend weekly). The SBC is Baptist in name and practice but about 99% of the other 45 million American evangelicals are also Baptist in theology, piety, and practice if not in name. This reality shapes the way Americans tend to think about baptism, the way they read and interpret Scripture, and the way they understand the message of Scripture. From a historical point of view, our situation in anomalous. Until the middle of the 19th century the situation was reversed. Prior to the middle of the 19th century, the overwhelming majority of Christians worldwide and even in the USA were paedobaptist, i.e., they baptized infants. Now, to be sure, they did so for different reasons. Romanists baptize infants because, in part, they believe that the mere use of the sacrament imparts saving, regenerating grace. Lutherans (both mainline and confessional) also confess that the use of baptism confers new life (regeneration). Mainline (liberal) denominations such as the PCUSA, the EPCUSA, the UMC, the UCC baptize infants mainly because it is traditional or out of sentiment.
What Baptism Does And Does Not Do
This sociological and historic reality creates challenges for those who still believe and confess the historic Reformed understanding of Scripture, that God has promised to be a God to believers and to their children (Gen 17:7), who do not baptize out of sentiment (“isn’t that nice”), tradition (“that’s the way we have always done it”), or because they believe that it necessarily confers saving saving grace to every baptized person (magic). In the Reformed understanding baptism is a sacrament, i.e., a sign of promised grace and a seal, a promise of saving grace to those who believe. To be sure, according to the Reformed confession, Christ is received sola gratia (by grace alone), sola fide through faith alone. Grace is not a magic or medicinal substance (Rome). Rather, it is the unconditional favor of God toward sinners earned by Jesus Christ for all his people. By grace alone God is favorable to all his people (composed of all sorts of people, from all tribes, languages, and nations) for the sake of the righteous (e.g., obedience) of Christ imputed (credited) to sinners and received through faith alone. By faith we mean, trusting, resting, receiving, knowing, and assenting. Baptism signifies what Christ does for his people (washes away their sins and clothes them with his righteousness) and seals the promises made to those who have new life, who believe that all that Christ has done for them. As a seal, it says to believers that what they have read in Scripture, what they have heard in the preaching of the Word is really truly theirs.
This is what we confess in Heidelberg Catechism (1563) 69:
69. How is it signified and sealed to you in Holy Baptism, that you have part in the one sacrifice of Christ on the cross?
Thus: that Christ instituted this outward washing with water and joined therewith this promise: that I am washed with His blood and Spirit from the pollution of my soul, that is, from all my sins, as certainly as I am washed outwardly with water, whereby commonly the filthiness of the body is taken away.
Against the Romanists and the Lutherans we confess explicitly that baptism does not, by its use (ex opere operato) become salvation any more than the bread and wine of communion literally become (by transubstantiation) the body and blood of Christ:
72. Is then the outward washing with water itself the washing away of sins?
No, for only the blood of Jesus Christ and the Holy Spirit cleanse us from all sin.
To put it plainly, a baptized person who does not believe is damned and an unbaptized person who, by grace alone, does believe has been saved.