Sin is simply the act of disobeying God, so by definition God can't commit a sin of omission, or any other kind for that matter.
You assert that there is no capability to resist temptation without the knowledge of good and evil. That is false. Adam and Eve had a choice. They didn't need to understand the dichotomy of good vs. evil to know that God, their creator, had instructed them not to eat the fruit. It's like saying you're child doesn't have the ability to listen to your instruction until he is old enough to understand the subject matter of the instruction.
If I tell my child not to hurt other children, it doesn't matter if he/she understands why...he/she is perfectly capable of listening nonetheless.