It seems that there is an assumption here that unless God chooses who will go to heaven, then people must suffer for their own sins (in Purgatory). Nothing could be further from the truth in evangelical Christianity.
The Scriptures teach that God declares righteous those who have faith in Jesus--even the ungodly. In doing so, their sins are completely forgiven--past, present, and future. "Therefore, there is now no condemnation" for them. They have been sanctified (made holy), so there is no future purging or purification that they need to gain by their own suffering.
"But to the one who does not work, but believes in Him who justifies [declares righteous]
the ungodly, his faith is credited as righteousness." Romans 4:5 NAS
This is the beauty of salvation, as Spurgeon discusses in his book, All of Grace. God takes an ungodly person and declares him righteous. Faith in Jesus is the channel through which righteousness is imparted to the ungodly one. The sinner is declared righteous--and righteous people have nothing to be purged of in Purgatory.
"Therefore there is now no condemnation for those who are in Christ Jesus. 2 For the law of the Spirit of life [a]in Christ Jesus has set you free from the law of sin and of death." Romans 8:1 NAS
There is no condemnation--none, zip, zero.
"For Christ also died for sins once for all, the just for the unjust, so that He might bring us to God, having been put to death in the flesh, but made alive in the spirit;" 1 Peter 3:18 NAS
Jesus died for sons once for all--not once and then there needs to be more suffering by us later, but once for all.
"For as through the one man’s disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous." Romans 5:19 NAS
It was the one act of righteousness performed by Jesus Christ that results in righteousness to those who trust in Jesus--it has nothing to do with our own works of righteousness, which merit nothing in God's sight.
So, the evangelical perspective which denies Purgatory and denies Predestination justifies the position by the doctrine of salvation itself. God offers salvation/justification (the declaration of righteousness) to all people who put their trust in Jesus. God does not require us to suffer for our own sins in Purgatory, because Jesus already suffered for them once for all. This salvation is available to "whosoever will."