Actually, as shown, it does not.
PS thou shall not eat of it does nothing at all to show Adam was a sinner before he ate.
The Law shows us we are sinners. This is elementary.
There is no difference between the Law of God and a Command of God. The Law of God are His Commands, and the Commands of God are Law.
8 But
sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead.
9 For I was alive without the law once:
but when the commandment came, sin revived, and I died.
10 And the commandment, which was ordained to life, I found to be unto death.
11 For sin, taking occasion by the commandment, deceived me, and by it slew me.
12 Wherefore the law is holy, and the commandment holy, and just, and good.
Romans 7: 8–12.
By God commanding "thou shalt not eat of it (the Tree)," shows that Adam and the woman were sinners just as Saul explains above in Romans.
Adam and the woman were created sinful, that is, "missing the mark" (which is the definition of sin according to Strong.) What is the "mark" that these two "missed"?
The glory of God. They were created fallen short of the glory of God.
And although they were created sinful, their sin did not revive until God said, "Thou shalt not eat of it (the Tree.)"
Adam and the woman for however long before the test of the Tree of the KNOWLEDGE of Good and Evil came to be lived a blissful life knowing only "good" because there was no restriction that would prove they were sinful. All God was doing was giving the man and woman the KNOWLEDGE of their sinfulness. When the Command came, sin revived in them, and they died. They died because they were created sinful and with the command came their KNOWLEDGE of their sinfulness.
THAT'S how the test went. God used the Tree to show them they were sinful. And even if there was no test, in time - maybe 900 years they would have eventually died because they were not created eternal. In this alone shows they fallen short of the glory of God because they were not eternal.
The comparison is Christ, the last Adam. He was sinless, He was Holy, He was Righteous, nor was guile found in His mouth. And being EQUAL to God He could stand before a Holy God blameless.
But not the man or the woman. They were not eternal. Example: Jesus Christ could possess ALL the Attributes of Deity and be able to stand before God blameless. But if Jesus Christ was not eternal, then by that one lack He would be judged as being fallen short of the glory of God.
It's not hard to understand.