Paul's argument with those who insist that the gentiles must become beholden to Torah is that the Torah was not given to make anyone righteous but rather to turn sins into crimes and that those crimes led to a death sentence (KJV: "condemnation"). In 5:12 he is introduces this discussion of how those beholden to Torah earned death in addition to the separation from the tree of life brought about by Adam.
What makes the difficult to the reader of Romans 5:12 is the failure to recognize that verse 12 is the beginning of a point he is going to explain in the verses that follow. The other things one needs to read the passage properly is to recognize that "condemnation" does not mean "God shames people" but rather that people come under a death sentence. Also, a "transgression" is different from a "sin". A "sin" is a wrongdoing, but a "transgression" is a crime, with a sanction/punishment attached. Without understanding that vocabulary, you miss the point.
Paul explains that the gentiles are all subject to death (separated from the tree of life) because of Adam's single transgression but those beholden to Torah are condemned to death a thousand times over because of their transgressions against Torah:
[Dan 9:11 KJV] (11) Yea, all Israel have transgressed thy law, even by departing, that they might not obey thy voice; therefore the curse is poured upon us, and the oath that [is] written in the law of Moses the servant of God, because we have sinned against him.
[Rom 5:13-21 NLT] (13) Yes, people sinned even before the law was given. But it was not counted as sin because there was not yet any law to break. (14) Still, everyone died--from the time of Adam to the time of Moses--even those who did not disobey an explicit commandment of God, as Adam did. Now Adam is a symbol, a representation of Christ, who was yet to come. (15) But there is a great difference between Adam's sin and God's gracious gift. For the sin of this one man, Adam, brought death to many. But even greater is God's wonderful grace and his gift of forgiveness to many through this other man, Jesus Christ. (16) And the result of God's gracious gift is very different from the result of that one man's sin. For Adam's sin led to condemnation, but God's free gift leads to our being made right with God, even though we are guilty of many sins.[G: transgressions παραπτωμάτων] (17) For the sin of this one man, Adam, caused death to rule over many. But even greater is God's wonderful grace and his gift of righteousness, for all who receive it will live in triumph over sin and death through this one man, Jesus Christ. (18) Yes, Adam's one sin brings condemnation for everyone, but Christ's one act of righteousness brings a right relationship with God and new life for everyone. (19) Because one person disobeyed God, many became sinners. But because one other person obeyed God, many will be made righteous. (20) God's law was given so that all people could see how sinful they were. But as people sinned more and more, God's wonderful grace became more abundant. (21) So just as sin ruled over all people and brought them to death, now God's wonderful grace rules instead, giving us right standing with God and resulting in eternal life through Jesus Christ our Lord.
All of this, therefore, is directly relevant to his entire polemic/teaching against requiring Torah observance for gentiles.