If the believer, who believes in Christ, the Christ who died for our sins and nailed them to the cross as a one time sacrifice for all of our sins, is not cleansed by his belief in Christ, as described in the NT, then nothing remains that can forgive sins.
Without the shedding of blood, there is no remission of sins.
*Purgatory* can’t do it because suffering is not how our sins are dealt with.
It’s the wrong method for dealing with sin, and we can’t pay for our sins ourselves.