Whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed, to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus. (Romans 3:25-26)
God set Jesus forth as a propitiation by His blood. In doing this, God’s righteousness is demonstrated (Romans 1:17).
Paul’s point is: God is perfectly right and just to provide forgiveness to sinners through faith in Jesus Christ by His blood.
God’s righteousness is demonstrated.
Remember, sin's wages are death (Romans 1:32; Romans 6:23). So if sinners rightly deserve death, how can God rightly offer anything different?
Paul will point out that through Jesus’ sacrifice on the cross, God demonstrates His righteousness in justifying sinners.
God’s justifying of us must itself be just. It will hardly do for God to free us from our unholiness and unrighteousness by an unrighteous procedure. God is “law-abiding.” The Judge of all the earth will do right! said Abraham. - McGuiggan, Romans, 130
Jesus is the key to God “passing over the sins” previously committed. God did not ignore mankind’s sins before Jesus came to earth and died. Paul points out that God always had the death of Jesus in mind - even back in ancient times.
By making Jesus the means of atonement, God proved He was righteous by passing over sins committed in the past under the old covenant. God did not come down hard on these sins, as He could have, but waited until those sins could be covered by the blood of Christ (Hebrews 9:15). - Pollard, Truth for Today Commentary, 126
The argument is that God did something to demonstrate he was “just” in passing over sin. That something was to have Christ serve as a propitiation. His blood flowed back to those living prior to the cross. In like manner, His blood flows forward to every successive generation. Thus, God is “just while justifying him that believes in Jesus.” - Wacaster, Studies in Romans, 130
In fact, Jesus’ sacrifice was proof that God still cared for Israel. God would continue to offer His love and mercy to them - and all people - through His Son, Jesus Christ.
For those who thought God had abandoned His people, this would have been a confirmation of God’s continuous love for Israel. What He had done for Israel in the past, He also would do in the present through Christ (see 3:21-22). For Gentiles, it was also their chance to have forgiveness. - Pollard, Truth for Today Commentary, 127
Jesus satisfied God’s demands as Judge and our needs as sinners. Jesus died as the Lamb offered in our place (2 Corinthians 5:21).
God does not sweep His justice under the rug in offering us forgiveness. God is entirely just in offering justification by the blood of Jesus Christ (Romans 5:9).