If sin was not taken into account until Moses (the time come when there is law), then all that died up to then died solely on the account of death being in the world, yet death passed on to all men because all sinned... This begs the question then, who was or was not doing any accounting?
It's a tough subject, but here are a few tidbits that come to mind:
There was God's law prior to Moses/Sinai.
Because that Abraham obeyed my voice, and kept my charge, my commandments, my statutes, and my laws. Gen 26:5
(God to Cain)
... sin lieth at the door. And unto thee shall be his desire, and thou shalt rule over him. Gen 4:7 In order for Cain to rule over sin (a transgression of the law), he would first have to know the standard for that ruling (the law). This happened when Cain was "wroth" because God didn't respect his offering. Cain would have known that if he were angry at God for any reason, the fault would have to be his own.
In Romans 1:29-32 there is a list of 23 explicit sins that every man knows via God's direct revelation ("in them", v.19). These people "know God's judgement" and they know the verdict & sentencing: "worthy of death". They have the "work of the law" written in their hearts (2:15).
I believe people's (own personal) sins WERE imputed to them because there WAS God's law. They hadn't sinned after the similitude of Adam's transgression - but they sinned their own sins.
(Newborns, on the other hand, don't have the law. Even though the subject of babies appears to be beyond the scope of what Paul's talking about in Rom. 5; it can still be extracted from that text).
The fact that, after entering through Adam's sin, death reigned may provide an answer for that. Adam rendered all men subject to death, but would it require a leap over a gap in logic to claim that Adam rendered all men subject to sin? I'm not so sure that it does. Susceptible, surely, I can't find reason to argue that. But as long, as there was one man that did not bow his knee to sin, then I can't confidently claim that "all men are subject to sin."
For as by one man's disobedience many were made sinners ... (Romans 5:19) I think the reason "many" is used instead of "all" is that Paul is establishing a parallel in the 2nd part of the verse that requires "many":
... so by the obedience of one shall many be made righteous. (The previous verse (18) does use "all" in both sides of its parallel.) But it shows that Adam's disobedience wasn't just the cause of death, but also of people being made sinners.
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