You raise a very interesting point here that needs further examination.
I am inclined to believe the woman was the first to commit an actual sin of practice. This falls in line with the passage from 1 Tim 2:14 (Adam was not deceived, but the woman was deceived and became a transgressor.)
However 1 Tim 2:14 raises another question. Clearly Eve was deceived by the serpent in the garden. (See Gen 3). However, if you examine that conversation between Eve and the serpent, you will notice that Eve added to the command of God "neither shall you touch it" (3:3)
Where did Eve get this additional information? God spoke to Adam in Gen 2:15-17 about the tree in midst of the garden, and told him "of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.”
Notice the following truths about this passage. First, there is nothing in the statement from God about not touching the tree or the fruit of it. Second, and I think more important for this discussion, Eve was not here! In fact Eve is not formed until the next passage. (Gen 2:18-22)
So, the question I referenced earlier is this. Where did Eve get the idea that she should not even touch the tree, lest she die? The serpent did not suggest it, the words were first spoken by Eve. The only record of the command of God not to eat of the tree was given to Adam.
I submit that Adam told Eve not to eat, but added not to touch. (If you never touch it you cannot ever eat it). So, Eve was deceived because Adam added to the command of God. BUT I HAVE MORE.
Going back to 1 Tim 2:14 - Read it again.. Adam was not deceived. STOP THERE. Adam sinned willingly and with full knowledge of what he was doing. At least Eve has some type of excuse, deception. Adam had NONE!
Not only did Adam sin deliberately, but returning to Gen 3 it says the Eve gave the fruit to Adam "who was with her" (3:6). Adam was right there watching all of this transpire and did nothing to stop it.
So, which is the more grievous sin? One that the person was deceived into committing? Or one that a person commits with full knowledge of and deliberate intent? Do you really want to follow someone that 1) added to the word of God? 2) that sees sin transpiring and does nothing to stop it. 3) That willfully, knowingly, deliberately, sins?
Now, back to the woman question. If a woman is disqualified because of being deceived into sin, how does a man who intentionally and deliberate sin provide a better option?