(IFF) your hypothetical god is really really realzies (THEN) it doesn't matter what you or I or anyone thinks about it.
Sure it matters. Then it matters whether you believe in this God or not. Then it matters in that God provides the necessary best that morality is based upon. Then it matters whether or not you believe in the one means God has given that reconciles us to Him. And a thousand more things.
Insisting "it matters" is a bald assertion and an appeal to ignorance.
IFF this God exists it matters for He has disclosed it matters. You made up a logical statement on the IFF. I responded to your scenario even though I believe it is not hypothetical that God exists as you do. So I responded to your logic with THEN statements in correspondence and response to your original premise.
(IFF) your hypothetical god is omnipotent and omniscient and the sole origin and creator of all things (THEN) we are exactly what god intended, each one of us is a perfect representation of god's infinite wisdom.
No, we are not what God intended since the Fall. God intended the human to choose whether he wanted a loving relationship with God. God created the human being as 'good,' yet with the ability to choose. We disobeyed God in Adam. Adam was our federal head. He represented us. Adam determined the outcome by his actions and God permitted him his choice and the consequences.
And before you go all, free-willy on me, please understand that,
(IFF) free = uninfluenced (AND) (IFF) will = goal-seeking (THEN) it is impossible for any action to be BOTH free and willed.
There again, Adam had free will. We do not in the sense that our wills are influenced by any number of factors, one of which is that we do not want a relationship with God. The Bible reveals the "natural man" does not seek God. That is why Jesus said we must be born again. We need a chanced mind towards God. That comes from His revelation, His word, His Spirit at work in our life, His Son. As natural people, I believe we seek what we desire rather than what is good to a large degree. We want to be autonomous.
Any free action must necessarily be indistinguishable from a random action.
As I said, we have volition, a will, and we choose yet our desires are selfish. Our goal is sided towards our own selves.
Any willed action must necessarily be influenced (motivated by desire and influenced by an imagined outcome).
True, it is influenced. The only persons who had the possibility to not sin were Adam and Eve. That was before the Fall. They had the choice to sin, or to not sin. Adam's choice affected us. Our natures have changed with the Fall. We sin and have a propensity to sin. We inherit that nature of disobedience from them. Once God was ignored and they chose to know evil they were distanced from the purity and holiness that is God. They started to do their own thing with themselves as their guides. They no longer had the witness and example of God. He withdrew.
Now, we choose to sin and cannot avoid sinning. That possibility is no longer an option. If you think it is, then try for a week not to lie, not to steal, not to covet, not to commit adultery in your mind, to hate (which Jesus likened to murder) for the same malice is present in those who murder.