More Jewish sources of the idea of the original sin...
"Now Oved begot Jesse, who was called Nahash, because no corruption and perversion, for which he might be delivered into the hands of the angel of death, who would take his life from him, were found in him. He lived a long time, until the
serpent's counsel to Eve, Adam's wife, to partake of the fruit of the tree, the eating of which resulted in wisdom to distinguish between good and evil, was recalled before God. Because of that counsel, all inhabitants of the earth are mortal, and as a result of that blunder, the righteous Jesse died. He is Jesse, who was the father of David, the king of Israel." Targum Ruth 4:22
"Our Rabbis taught: Four died through the counsel of the serpent, namely, Benjamin son of Jacob, Amram the father of Moses, Jesse the father of David, and Kilab the son of David." Bava Basra 17a
The Soncino footnote explains the meaning of the phrase "the counsel of the serpent," "The counsel given by the serpent to Eve, which brought death on all mankind, and not for any sin they themselves committed.
"For, indeed,
"there is not a righteous man upon earth that doeth good and sinneth not" (Eccl. 7:20). And even the sinless ones who only died because of the "counsel of the Serpent" will arise and be counselors to the Messiah." Zohar II:54a
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"R. Yesa said: Adam appears to every man at the moment of his departure from life to testify that the man is dying on account of his own sins and not the sin of Adam, according to the dictum, 'there is no death without sin'. There are only three exceptions, namely, Amram, Levi, and Benjamin, who were deprived of life through the prompting of the primeval serpent; some add also, Jesse. These did not sin, and no ground could be assigned for their death save the prompting of the serpent, as we have said." Zohar I:57b
"Bnei Yisrael were susceptible to the arrogance of Egypt, only because the seeds of arrogance that had already been planted within them by Adam's sin. Since the souls of all mankind were included in Adam's soul, we were all party to his sin, and we are all still marked by its effect. Through our Torah and mitzvos, we strive to correct Adam's sin, which sullied the entire human race with arrogance. . . The ultimate perfection of human character will occur with the coming of Moshiach, when Adam's sin of arrogance will be entirely corrected. In this merit, we will finally be able to understand the deepest secrets of the Torah, of which the Midrash states: "The Torah that man learns in this world is like mist compared to the Torah that will be taught by Mashiach (Messiah).
Mevaser Tov, The Biala Rebbe, Sefirat HaOmer, pg. 251
"And it shall be when the sons of the woman consider the Torah, and perform (its) instructions, they will be prepared to smite you on your head to kill you. But when the sons of the woman forsake the commandment of the Torah, and perform not (its) instructions, you will be ready to wound them in their heel, and hurt them. Nevertheless there shall be a medicine for the sons of the woman, but for you, serpent, there shall be no medicine. However, for these there shall be a remedy for the heel in the days of the king Meshiha." Targum Jonathan on Genesis 3:15
Targum are Aramaic translations of the Tanakh. Jonathan's and Onkelos' are the two most popular Onkelos's Targum was written during the 1st century and Jonathan's in the second century.
I have now provided 5 different sources of the concept of Adam's sin effecting all mankind. All 5 sources are independent of each other. All sources are completely Jewish....Orthodox Jewish.