There's really no getting around it. OP is correct, the first act of infidelity did occur in the garden of Eden between Satan and Eve. This is why the Lord said to Satan:

"...I will put enmity between you and the woman, and between your seed and her Seed."[Gen.3:15]

"Your seed" represents children born from adultery and fornication. And "her Seed" represents the Lord Jesus Christ, as well as all children born within the marriage covenant. It's wicked and selfish to deliberately choose to have children outside the marriage covenant! This is how the World gets filled with devilish seed instead of godly seed. The Devil knows this that's why he hates the marriage covenant so much.

Satan did not father Cain! He did, however, defile Eve. As a result, he defiled the marriage covenant! And that's why Adam shouldn't have had sex with Eve, once she was defiled. Because he did, Adam's first born, Cain, was a profaned seed.

Sexual intercourse within the marriage covenant is represented in Scripture as eating good fruit, while fornication and adultery is represented by eating bad fruit.

"Like an apple tree among the trees of the woods, So is my beloved among the sons. I sat down in his shade with great delight, And his fruit was sweet to my taste." [Songs of Sol.2:3]

Once Eve had been defiled by Satan, Adam also defiled himself by having sex with Eve. For as the first Man, Adam was the Priest of the Human race. And it's strictly forbidden for a priest to have sexual intercourse with a woman who has been defiled!

"And the Lord said to Moses, “Speak to the priests...They shall not take a wife who is a harlot or a defiled woman...he shall take a wife in her virginity. A widow or a divorced woman or a defiled woman or a harlot—these he shall not marry; but he shall take a virgin of his own people as wife. Nor shall he profane his posterity among his people, for I the Lord sanctify him.’” [Lev.21:1,7,13-15]

Adam didn't take Eve in her virginity, as a consequence, he profaned his posterity through Cain. And what so tragic is that up until this very day, hundreds of millions of men, all claiming to be Christians, are still profaning their posterity through adultery. May God have mercy on their souls!