Yes, that "through one man , sin entered the world" according to Romans 5:12.
"Results of Sin. Eve was thoroughly deceived by Satan the Devil, but “Adam was not deceived,” says the apostle Paul. (1Ti 2:14) With full knowledge Adam willfully and deliberately chose to disobey and then as a criminal he tried to hide. When brought to trial, instead of showing sorrow or regret or asking for forgiveness, Adam attempted to justify himself and pass the responsibility off on others, even blaming Jehovah for his own willful sin. “The woman whom you gave to be with me, she gave me fruit from the tree and so I ate.” (Ge 3:7-12) So Adam was cast out of Eden into an unsubdued earth that was cursed to produce thorns and thistles, there to sweat out an existence, harvesting the bitter fruits of his sin. Outside the garden, awaiting death, Adam fathered sons and daughters, the names of only three being preserved—Cain, Abel, and Seth. To all of his children Adam passed on hereditary sin and death, since he himself was sinful.—Ge 3:23; 4:1, 2, 25.
This was the tragic start Adam gave the human race. Paradise, happiness, and everlasting life were forfeited, and in their place sin, suffering, and death were acquired through disobedience. “Through one man sin entered into the world and death through sin, and thus death spread to all men because they had all sinned.” “Death ruled as king from Adam down.” (Ro 5:12, 14) But Jehovah in his wisdom and love provided a “second man,” “the last Adam,” who is the Lord Jesus Christ. By means of this obedient “Son of God” the way was opened up whereby descendants of the disobedient “first man Adam” could regain Paradise and everlasting life, the church or congregation of Christ even gaining heavenly life. “For just as in Adam all are dying, so also in the Christ all will be made alive.”—Joh 3:16, 18; Ro 6:23; 1Co 15:22, 45, 47.
After sinner Adam’s expulsion from Eden he lived to see the murder of his own son, banishment of his killer-son, abuse of the marriage arrangement, and profanation of Jehovah’s sacred name. He witnessed the building of a city, the development of musical instruments, and the forging of tools out of iron and copper. He watched and was condemned by the example of Enoch, “the seventh one in line from Adam,” one who “kept walking with the true God.” He even lived to see Noah’s father Lamech of the ninth generation. Finally, after 930 years, most of which was spent in the slow process of dying, Adam returned to the ground from which he was taken, in the year 3096 B.C.E., just as Jehovah had said.—Ge 4:8-26; 5:5-24; Jude 14; see LAMECHNo. 2."
Why do you say it was Eve?
"Paul outlined the matter, starting with this point: “Through one man sin entered into the world and death through sin, and thus death spread to all men because they had all sinned.” (Rom. 5:12) We are in a position to understand this because God had a record made of how human life began. Jehovah created two humans, Adam and Eve. The Creator is perfect, and so were those first humans, our ancestors. God gave them but one limiting directive and informed them that disobeying that law would bring a death sentence. (Gen. 2:17) However, they chose to act ruinously, violating God’s reasonable directive, thus rejecting him as Lawgiver and Sovereign.—Deut. 32:4, 5.
6. (a) Why did Adam’s descendants die both before God gave the Mosaic Law and thereafter? (b) What can be illustrated with a disease like hemophilia?
6 It was only after Adam had become a sinner that he fathered children, passing on sin and its effects to all of them. Of course, they had not violated the divine law as Adam had, so they were not charged with the same sin; nor had any law code yet been given. (Gen. 2:17) Still, Adam’s descendants inherited sin. Thus, sin and death ruled down to the time when God gave the Israelites a law code, which clearly showed that they were sinners. (Read Romans 5:13, 14.) The effect of inherited sin might be illustrated with certain inherited diseases or defects, such as Mediterranean anemia or hemophilia. You may have read that Alexis, son of Russian Czar Nicholas II and Alexandra, inherited the bleeding disorder hemophilia. Granted, even in such a family, some children do not suffer from those diseases, but they still may be carriers. Not so with sin. The defect of sin from Adam was inevitable. All are subject to it. It is always fatal. And it is passed on to all children.