So, Eve had a desire to eat which was not allowed. So, she already committed the sin even before she ate. Adam followed to eat. As such, we can only conclude that Adam and Eve were created with sin.
What created the deadly desire in Eve was the belief that God was a liar. People typically act consistently externally with their beliefs that are internal. Eve chose not to believe God.
Disbelief precedes sin and causes it.
For whatever does not proceed from faith is sin. - Romans 14
Disbelief is the culprit here, not God. True, God did create free will, but Eve could have just as easily believed that God was not a liar.