“We assert that the whole guilt of sin is taken away in baptism, so that the remains of sin still existing are not imputed. That this may be more clear, let my readers call to mind that there is a twofold grace in baptism, for therein both remission of sins and regeneration are offered to us. We teach that full remission is made, but that regeneration is only begun and goes on making progress during the whole of life. Accordingly, sin truly remains in us, and is not instantly in one day extinguished by baptism, but as the guilt is effaced it is null in regard to imputation. Nothing is plainer than this doctrine.”
Now, in context, Calvin is rejecting how another sacrament is needed after baptism to deal with sin. But note what he assumes: remission and regeneration are conveyed in baptism. The Protestant protest against Rome does not reject that baptism conveys the grace of remission of sins, but insists it only comes to those with true faith. It is not an automatic, dispensed by the "vending machine" church.
For more proof of that, consider what Westminster says on baptism: "The efficacy of Baptism is not tied to that moment of time wherein it is administered; yet, notwithstanding, by the right use of this ordinance, the grace promised is not only offered, but really exhibited, and conferred, by the Holy Ghost, to such (whether of age or infants) as that grace belongs unto, according to the counsel of God's own will, in His appointed time." (John 3:5-8; Gal 3:27; Titus 3:5; Eph 5:25; Acts 2:38)
Here is the link to Calvin's whole response. It is very long! The quote above is in the fifth statement.