Again, context requires we read the whole Bible, and not just pull one verse out of context. In fact, Adam was to blame for sin entering the world, because he deliberately disobeyed God. Eve was not even created, according to Genesis 2: when God gave the command not to eat of the tree.
"The Lord God took the man and put him in the garden of Eden to work it and keep it.16 And the Lord God commanded the man, saying, “You may surely eat of every tree of the garden,17 but 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.”18 Then the Lord God said, “It is not good that the man should be alone; I will make him a helper fit for him.” Genesis 2:15-18
Eve was deceived, but Adam disobeyed, the worst sin of all!
"Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all menbecause all sinned." Romans 5:12
Who was that one man? Adam!
"Yet death reigned from Adam to Moses, even over those whose sinning was not like the transgression of Adam, who was a type of the one who was to come." Romans 5:14
The fact is, we are all in this together. women are not punished more or less than men for either the first sin, or the sin we all do in life.
"There is neither Jew nor Greek, there is neither slavenor free, there is no male and female, for you are all one in Christ Jesus." Gal 3:28
Our hope is in Jesus Christ, who died on the cross and made atonement for sin. No one is deserving of salvation, but whoever calls on the name of the sordid will be saved!
"For “everyone who calls on the name of the Lord will be saved.” Romans 10:13
It is not who sinned first, or worse, but ALL have sinned and fall short of the glory of God!
"for all have sinned and fall short of the glory of God." Romans 3:3
But, we have a Saviour! Let's look to him instead of this fruitless exercise in judging and blaming!
"Now to him who is able to keep you from stumbling and to present you blameless before the presence of his glory with great joy,25 to the only God, our Savior, through Jesus Christ our Lord, be glory, majesty, dominion, and authority, before all time and now and forever. Amen." Jude 24-25