In v12 it is clear Paul is referencing Adam as the one man who brought sin into the word. Some argue it is impossible for humans to have existed prior to Adam and yet Adam be the first sinner. This assumes a broad definition of sin in Rom 5:12. So it is appropriate to inquire what is “sin” in this context?
I suggest the definition of 1John 3:4 “sin is the transgression of the law” is appropriate to the context being similar in thought to Rom 4:15. Plus it is clear from Rom 5:13 that we are talking about sin in the context of a law being given (and how these principles are then extended to cover those outside of the law as Paul goes on to explain). Verse 20 also makes clear Paul’s use in this pericope is very much sin as conscious transgression.
In addition to the context of v13, further evidence for this understanding is provided by Moo who observed:
“The fact that Paul attributes to Adam this sin is significant since he certainly knows from Genesis that the woman, Eve, sinned first (cf. 2 Cor. 11:3; 1 Tim. 2:14). Already we see that Adam is being given a status in salvation history that is not tied only to temporal priority.”
Ie Eve ‘fell short of God’s glory, she was the first to break the commandment. But Paul says the first sin was Adam’s. Paul does distinguish between Adam & Eve when he bases teaching on Gen 2-3 so we can’t claim the two were treated as one in his theology. From 1 Tim 2:14 it is evidence Eve was deceived but Adam committed the first deliberate/conscious sin. When people argue for a broad definition of sin (coming short of God’s glory) to ‘prove’ there could not have been people outside the garden (see for example The Lampstand Volume 23, N0 3 page 145 – June 2017), they effectively make Paul contradict himself.
Paul is making a point of the contrasting men – Adam and Christ. His choice of Adam provides positive evidence Paul is not using sin in the sense of ‘falling short of God’s glory’ but rather a deliberate transgression, a conscious breaking of the law. This fits the later verses where Paul will deal with men without accountability to law being accounted sinners. If the definition of sin here was a broad one this accounting would be unnecessary.
We ought also to be clear on what Paul is NOT saying. He is not talking about sin as a state of being or as our nature – his focus is on a specific action. Paul is talking about accountable/conscious sin as a transgression of law – Adam was the first transgressor.
 Moo, D. J. (1996). The Epistle to the Romans (p. 319). Grand Rapids, MI: Wm. B. Eerdmans Publishing Co.