The Law of sin and death, and no, it did not pop into existence at the time of Moses. We see it played out in the Garden.
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.
Romans 1 sheds light on man's accountability from the get-go:
Romans
1:20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse:
1:32 Who knowing the judgment of God, that they which commit such things are worthy of death, not only do the same, but have pleasure in them that do them.