Adam had free will. He exercised it poorly that day.
The issue throughout Scripture as to man's stumbling is ever the same - his failure to exercise his free will and simply take God at His Word.
In Adam's case, however, by his own failure in that, that day, all were made sinners.
His transgression that day, a kind of a baptism into the spiritual death of transgression; a spiritual union with, an identification with trangression that day.
Something in him changed with that.
Something which, as with that change in a parent that results, say, in a crack or an HIV baby, could not but be passed on to Adam's offspring.
The result being that although sin is not imputed where there is no law, there is still this issue of this nature man is born with that is corrupt.
And corruption can not inherit incorruption.
Baby's and toddlers are not held to account because they do not know how to discern right from wrong.
Thus, they are cleansed from that based on their ignorance, not on their supposed innocence.
Numbers 15:28 And the priest shall make an atonement for the soul that sinneth ignorantly, when he sinneth by ignorance before the LORD, to make an atonement for him; and it shall be forgiven him.
Which is really the greater issue determining that one - the greater issue in the case of babies and toddlers - of their not knowing to discern between things that differ.
Sort of like how the Son had been able to pray the Father forgive Israel's not having been able to discern the difference in things that differ such that they had not been able to discern the time of their visitation (though punished they would be for it, upon their being made aware of their having been ignorant, only to reject said awareness).
Til then, His murder, overturned by the Father to a charge of manslaughter, and an OFFER of pardon (And now, brethren, I wot that through ignorance ye did it, as did also your rulers...Repent ye therefore...Acts 3:17, 19).
Result being that man has to be made conscience that he has a kind of an AIDS in him.
Which, as with the child born to Alcoholic parents, is basically dormant within that child...until it is set off by context and circumstances similar to those which in its' Alcoholic Parents, sets off their compulsion.
Said offspring going about its' merry way, ignorant of this dormant nature within it...til the right context and or circumstances, set it off.
I had not known (been aware of dormant, indwelling) sin (within me), but by the law...But when the commandment came, sin revived, and I died.
"I'm sorry, there is nothing we can do...He was born an alcoholic; it's a part of his very genetic makeup; he will struggle with that his entire life.
Does not have to be our predicament though...
Romans 7:13 Was then that which is good made death unto me? God forbid. But sin, that it might appear sin, working death in me by that which is good; that sin by the commandment might become exceeding sinful. 7:14 For we know that the law is spiritual: but I am carnal, sold under sin.
7:18 For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
7:20 Now if I do that I would not, it is no more I that do it, but sin that dwelleth in me.
That is then.
This is now.
Romans 8:2 For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.
2 Corinthians 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
Made Him to BE SIN for us.
Uh oh...
Ezekiel 18:4 Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die.
Matthew 26:38 Then saith he unto them, My soul is exceeding sorrowful, even unto death: tarry ye here, and watch with me.
Matthew 26:39 And he went a little farther, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.
Luke 12:50 But I have a baptism to be baptized with; and how am I straitened till it be accomplished!
Galatians 3:13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
Hebrews 2:9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man.
Romans 5:6 For when we were yet without strength, in due time Christ died for the ungodly. 5:7 For scarcely for a righteous man will one die: yet peradventure for a good man some would even dare to die. 5:8 But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. 5:9 Much more then, being now justified by his blood, we shall be saved from wrath through him. 5:10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life. 5:11 And not only so, but we also joy in God through our Lord Jesus Christ, by whom we have now received the atonement.
Romans 6:12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. 6:13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. 6:14 For sin shall not have dominion over you: for ye are not under the law, but under grace.