I suggested in another discussion that the first humans sinned by desiring the fruit of the forbidden tree (Gen 3:6). The Hebrew word for "to desire," (חָמַד) is the same word (although different form) translated "to covet" in the commands against it.
While this word can be used in a good sense, such as its use in Gen 2:9 for all the desirable trees in the garden; it is usually used in negative senses - to desire what one should not have. It is clear in the context that Eve should not eat of the forbidden tree in the garden.
As Jesus points out in Matthew 5, our inner desires, when focused on things we shouldn't do, are sins.
Thus, I posit that the first sin of the humans was their desire to eat what God had forbidden. That came before the act of eating the forbidden fruit.
Interestingly (at least to me,) the LXX changes the verb, "to desire," into an adjective, "beautiful." Where the the ESV has "the tree was to be desired to make one wise," the LXX (NETS) has "it was beautiful to contemplate" [ὡραῖόν ἐστιν τοῦ κατανοῆσαι]. Could she have been obsessed with the beauty of this one tree and fruit?
If this desire for what was forbidden was part of their nature/essence before the sinful act, what might that indicate about our understanding of pre-fall life? I remember a speaker pointing out that the while the first creation account often says, "It was good," the second account (from which Gen 3 also comes,) has God saying, "It is not good" (Gen 2:18).