Was Adam's rebellion the first sin?

Good question.

When I read your question, I immediately thought about James Chapter 1, where we read,

Let no one say when he is tempted, “I am being tempted by God”; for God cannot be tempted by evil, and He Himself does not tempt anyone. But each one is tempted when he is carried away and enticed by his own lust. Then when lust has conceived, it gives birth to sin; and when sin is accomplished, it brings forth death.

You'll see the relevance of those verses shortly.

First, however, let's define some key terms. Rebellion, as you've used the term, certainly describes Adam's sin, but biblically Adam's sin was disobedience.

For as through the one man’s disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous (Romans 5:19 NASB).

Second, one reason for Adam being depicted as the fall guy (no pun intended) instead of Eve is found in the biblical teaching on headship. Without going into a great deal of detail here, from the beginning, man was the head of the woman, much like Christ is the head of the Church Universal (Ephesians 5:23; Colossians 1:18).

In a day of political correctness, the concept of headship seems to many to be primitive--offensive, even. Significantly, the Bible's teaching on headship does not even imply remotely that woman is in any way inferior to man. The Bible teaches clearly they are equals in God's sight. God is not a respecter of persons (Acts 10:24; cf. Galatians 3:28).

The Bible also teaches, however, that from the beginning the man was accountable to God in a way the woman was not. Were both Adam and Eve culpable of disobedience? Yes. Clearly, Eve was no less culpable than Adam. Nevertheless, Adam was held accountable in ways which Eve was not.

What did God say in the wake of the couple's disobedience?

And the Lord God called unto Adam, and said unto him, Where art thou? (Genesis 3:9 KJV, my italics).

Clearly, both Adam and Eve were guilty of disobedience. That Eve's disobedience was preceded by a process of deception is almost irrelevant to the more significant issue of her eventual disobedience.

Though not strictly biblical, there is a distinct possibility that Satan approached Eve more than once with the same temptation. Perhaps she weakened through multiple temptations by the adversary of her soul. Frankly, we do not know, nor will we ever know. What we do know, however, is that Adam was right there with her when she finally gave in to the the temptation of her advesary (who was, after all, the personage responsible for sin's entrance into the universe).

And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat (Genesis 3:6 KJV, my emphasis).

Where the Scriptures are silent we must not make unwarranted assumptions, but perhaps we are justified in surmising that had Adam "manned up," so to speak, and prevented his helpmeet (helpmate, or fit helper) from giving in to the temptation, there would not have been a fall from grace.

Still, Adam bore the brunt of blame in the fiasco. His sin, in a sense, was worse than his wife's, since in disobeying God, he betrayed his God-given headship.

While Eve's punishment, as with Adam's, was also death, she was to be burdened as well with the pain attached to childbirth.

Unto the woman . . . [God] said, "I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children; and thy desire shall be to thy husband, and he shall rule over thee" Genesis 3:16 KJV).

And from Paul's letter to his son in the Lord, we have these words,

For Adam was first formed, then Eve. And Adam was not deceived, but the woman being deceived was in the transgression (1 Timothy 2:14 KJV).

Two points in conclusion:

1. Being tempted is not sin; giving in to the temptation is. Temptation is a process, as James points out. We see (literally or figuratively), we want, we take. Lust entices us, carries us away, sin is birthed, and we are separated from God, some for a time and some forever.

2. Eve's deception took place prior to the Law being given through Moses. Bearing false witness--lying--was certainly a step in the wrong direction for Eve, but as James has pointed out, giving in to sin is a process. In the case of Eve, her deception itself may have been a long time in coming (as I've already suggested).

   Perhaps she gave in to Satan's enticements after being worn down over repeated exposures to the same temptation. We simply do not know for certain. Nevertheless, God did not hold Eve responsible for lying but for her disobedience, and with her disobedience, the weight of responsibility as the head of the woman, Adam became the titular head of all humankind.

   Albeit a clear anachronism of interpretation, from a 21st century perspective Adam carried in his body the "death gene." Through his seed each subsequent human being birthed into the world was infected with that gene.

"Behold, I was shapen in iniquity", the psalmist said, "and in sin did my mother conceive me" (Psalm 51:5 KJV)).

That sinful conception takes place in each generation because of Adam's "sin-and-death gene." While sin will always be, in a sense, taught, it is still an inborn capacity within the heart of each human being to disobey God. As has often been observed of children, no parent needs to teach his or her child to say no to mommy or daddy!

The good news, however, is that the "seed of the woman" (Genesis 3:15) would deal sin a death blow through the Son of Man, who because of his sinlessness could bear and take away the sin of the world.

Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed (1 Peter 2:24 KJV; cf. John 1:29 and 36).