Cloverdale Canadian Reformed Church

I think infant baptism is biblical. However, there is one question I have that I could not find any paedobaptist touching on, which is this: Can we say that God gives the same promises to all unbelievers afar off as they hear the gospel (Acts 2:39), whereas He wants the same promises to be visibly demonstrated on His covenant children upon birth? If not, what is the difference in the promises He makes? Thanks.