i wouldn't agree that the garden of God was Satan's domain -- i think his fall was previous to the creation of earth.
but, to the rest of your point, per 1 TImothy 2:14, Adam was not deceived, and it is Woman who was in transgression - if Adam was accountable for 'failing to prevent Woman from sin' then Adam was first in transgression, and you could accuse God of the same thing for failing to prevent either of them from sin.
there is a reason Satan went after Woman, instead.
whether he had tried & failed to deceive Adam previously, or just knew that he couldn't, is a matter of speculation - but we know that Satan did not deceive Adam.
but, to the rest of your point, per 1 TImothy 2:14, Adam was not deceived, and it is Woman who was in transgression - if Adam was accountable for 'failing to prevent Woman from sin' then Adam was first in transgression, and you could accuse God of the same thing for failing to prevent either of them from sin.
there is a reason Satan went after Woman, instead.
whether he had tried & failed to deceive Adam previously, or just knew that he couldn't, is a matter of speculation - but we know that Satan did not deceive Adam.
Adam's fault was his failure to truthfully relay God's warning to Eve. God told him in Gen 2:17: "But of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it, you shall surely die."
However, when Eve was asked about it, what did she reply? Gen 3:3: "But of the fruit of the tree which is in the midst of the garden, God has said, 'You shall now eat it, nor shall you touch it, lest you die."
Notice what Adam had added and omitted: God told Adam what that tree is, Adam skipped that part, and replaced it with the location of the tree; God only said you shall not eat it, Adam added "nor shall you touch it". That gave Satan an opportunity to manipulate Eve, to make her feel that God was hiding a secret from her, putting restrictions on her, withholding this power from her, and by that she fell to the temptation of tasting the forbidden fruit.