How was sin not counted before the law?

Genisis 3:5 & 22 - By eating the fruit of the tree of knowledge mankind gained knowledge of good and evil and blessing and calamity. As God knew humanity now had that knowledge, God held mankind accountable. That is the short answer.

Before Adam sinned by eating from the tree God commanded him not to eat he could have had fights with his wife, he could have hit her, lied to her about some things and not be guilty of any sin because he did not then have the knowledge of good and evil. If any of this happened then sin would be in the world but not be imputed to him.

Children also have an age of innocence before sin is imputed to them. Deuteronomy 1:39 speaks of the children of the Israelites who today have no knowledge of good and evil. In Romans 7:9 Paul says he was once alive without the law but when the commandment came, sin revived and I (Paul) died (spiritually). Now there is no way of knowing the exact age when a child becomes accountable for their own sins. It is probably different for every child but God the righteous judge would certainly know.

Law of conscience a Law unto itself

Conscience Vs. Law

Men ruled by conscience fall under the same; the law being written on their hearts, judging one another according to their own moral determinations. Paul establishes a relationship of equality with regard to law and conscience; both Jew, and Greek, in terms of an identical end result; the only possible exception sinlessness; in either case. In v.13 with respect to the law, it is "...doers of the law shall be justified.", and in v.12 it is implied in this "For as many as have sinned."

(Rom 2:12-16) "For as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law; (13) For not the hearers of the law are just before God, but the doers of the law shall be justified. (14) For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves: (15) Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another; (16) In the day when God shall judge the secrets of men by Jesus Christ according to my gospel."

Accounted

(Rom 5:12-16)  Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: (13)  (For until the law sin was in the world): but sin is not imputed when there is no law. (14)  Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come. (15)  But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. (16)  And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification.

If there is no difference, how is sin imputed? To those under the Law, judgment by the law which leads to death; and to those who exhibit the workings of law by nature, it being written on their hearts, as their conscience witnesses; death because of sin.

(Gal 3:18-19)  For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise. (19)  Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.

And that:

(Rom 7:13-14)  Was then that which is good made death unto me? God forbid. But sin, that it might appear sin, working death in me by that which is good; that sin by the commandment might become exceeding sinful. (14)  For we know that the law is spiritual: but I am carnal, sold under sin.

All have sinned

(Rom 3:23)  For all have sinned, and come short of the glory of God;

Why it is so amazing; God prevenient, in foreknowledge, had made provision for salvation apart from the Law, four hundred and thirty years before the Law was given; declaring that Christ was crucified from the foundation of the world; as here.

(1Pe 1:20)  Who verily was foreordained before the foundation of the world, but was manifest in these last times for you,

And here:

(Rev 13:8)  And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world.

That the Law testified of Jesus Christ, and does still, and that He being the very Word, and the recipient of the Promise given to Abraham, but made to Himself; and that he became the Law by fulfilling it, to die, and free, all who were under the curse of Adam, as well as those who were under the curse of the law; enjoined to them at Sinai. The Mountain quaked and smoked, and they said that they would fulfill all that the Lord had commanded.

(Exo 19:8)  And all the people answered together, and said, All that the LORD hath spoken we will do. And Moses returned the words of the people unto the LORD.

Men are not aware, who have had no such schoolmaster as the Law, and had no sense of any sin, imputed by a law they had never heard of. However, they had the visible workings of it, and the Law tells of the sin of Adam, by the effects of deviation; on all.

Sin is not imputed. Where there is not Law there is impunity; though the working of death is real unto this day because of sin.

but sin is not imputed when there is no law. This looks like an objection, that if there was no law before Moses's time, then there was no sin, nor could any action of man be known or accounted by them as sinful, or be imputed to them to condemnation; or rather it is a concession, allowing that where there is no law, sin is not imputed; but there was a law before that law of Moses, which law was transgressed, and the sin or transgression of it was imputed to men to condemnation and death...(Gill, John D.D. Dr. John Gill's Exposition of the Bible , (1697-1771) Pub. (1746-1766), 1816; public domain).