No human laws "pre-date" God's relationship with man.
The Bible says that God wrote His law in the hearts of men, and that man's own conscience bears witness against him. For instance, we have an example from the earliest time of murder, and the Bible makes clear that Cain knew it was morally wrong to kill Abel.
Man knows in his conscience that murder is wrong, so it is not surprising that so many civilizations have recognized murder as wrong. The Bible also says that when men ignore their consciences, it becomes desensitized ("seared with a hot iron"), and we have many historical examples of civilizations that have departed from God's principles.
This concept of "natural law" happens to be the fundamental premise upon which the founding of our own country was made.
How convenient. Without the least shred of evidence you attribute finely-evolved social instincts shared by all humans in all cultures since time immemorial to a diety for whom you have no evidence for existence.
I'll go you one better. The Flying Spaghetti Monster touched man's heart with His Noodly Appendage from the very beginning, writing His laws thereupon. And I have as much evidence for my story as you have for yours.
The Bible says that God wrote His law in the hearts of men, and that man's own conscience bears witness against him.
It sounds like you are saying something, but in reality there isn't anything useful there. You say all law is inspired by God, yet also allow that man-made law can fall short of God's will. So what can we conclude about any given law? Nothing. It could either be consistent or inconsistent with God's will.
Your original contention that all civilized law is based upon Judeo-Christian principles is contradicted by your own claim that societies can err. Therefore not all law is based upon true Judeo-Christian principles.
Historically, the percentage of people aquainted with the Judeo-Christian bible, let alone adhering to it, has been but a subset of the entire earthly population. Your escape around this historical divergence is to claim that everyone already knows all the laws, from the ancient Egyptians to the pre-Columbus American Indians, to the far eastern India Indians.
A simpler explanation is that certain "laws" have rather obvious joint benefits and rational creatures will discover and apply the obvious. No need for a lot of religious mumbo jumbo to explain the obvious.