Paul is talking to everyone, both believers and unbelievers. So, what judgment is he talking about that they will not escape? The answer is death because the scripture says that the judgment of God on sinners is death.
"For the wages of Sin is death..." (Romans 6:23a NASB)
The only reason we are not dead yet is His kindness and tolerance.
"Or are you despising the riches of His kindness and forbearance and patience, being ignorant that the kindness of God is leading you to repentance?” (Romans 2:4)
It is the "kindness of God" that leads us to repentance rather than the fear of what God might do to us.
"Repentance" is a word that means to stop and think about what you believe and where you are heading, and then turn around IF you find you are heading in the wrong direction.
"Repent, then and turn about for the erasure of your sins, so that seasons of refreshing should be coming from the face of the Lord..." (Acts 3:19)
We all need to think about what we believe about God from time to time - and be willing to turn around and head back toward the truth that God sacrificed His Son as the final sacrifice for the salvation of all humanity.
"...these things am I writing to you that you may not be sinning. And if anyone should be sinning, we have an Entreater with the Father, Jesus Christ the Just. And He is the atoning sacrifice for our sins, yet not only ours, but the sins of the whole world also." (1 John 2:1-2)
In Old Testament times, God laid all the sin of Israel upon a sacrificial animal once a year on the day of atonement, which cleansed the peoole of their sins from year to year. But that is no longer necessary because the blood of Jesus has "taken away the sin of the world". And His blood has redeemed and washed every sinner clean, both Jew and Gentile, believer and unbeliever, "for all time".
"Lo!, the lamb of God Which is taking away the sin of the world!" (John 1:29)
"…not through the blood of he-goats and of calves, but through His own blood, He entered once for all time into the holy places, finding eonian redemption." (John 1:29; Hebrews 9:12-26)
God is not the god of man made religions. Rather, He is a loving Father whose "kindness and tolerance and patience...leads you to repentance".
"Give thanks to the LORD, for He is good, For His lovingkindness is everlasting." (Psalm 136:1)
It is the realization of "the kindness of God" that leads religious folks to repent from worshiping a false god and embrace the gift of God.
"...the free gift of God is eternal life in Christ Jesus our Lord." (Romans 6:26)