These are the Mitzvoht that pre-date the commandments, The 10 Commandments and then the Code of Hammaurabi
Take the easiest to date Hammurabi, because we know pretty much when he lived and there are surviving stelae with information about him and these laws. From these the Code would date to about 1770 BCE
With the Mosaic Laws it is a lot more complicated because there is no evidence at all that the Egyptian called Moses who lead the Israelites ever existed. The earliest date I found for the Decalogue is 1400 BCE but it was first written down much later. Other scholars have pushed the date even close to our own time perhaps as late as 600 BCE
Traditionally the Laws of Abraham - a few of the Mitzvoht - have to be earlier than Moses. Abraham as the first of the Chosen has to precede Moses. But if Moses is complicated, Abraham is impossible especially as there is no evidence for Abraham either. Traditional dating puts Abraham's birth at 1800 BCE whilst Archbishop Ussher (of 4004 BC fame) puts it about 1976 BC. I have seen a date as early as 2018 BCE. All of these are pretty obviously fantasies that depend upon the various versions of the Old Testament, estimated dates of the Flood and impossibly long lifespans. The another difficulty is that the Bible is garbage. The earliest identifiable date for Abraham in the Bible would have had him associated with the Exile in Babylon, an event that (had it happened) would have been no earlier than 600 BCE others parts relate him to "Ur of the Chaldees," which could not be much earlier than 1000 BCE.
If you believe that the Bible is accurate then, technically, some of the Mitzvoht date back to the creation. Personally I go with Hammurabi especially as most of the OT laws seem derived from such codes.
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