If the Exodus didn't happen, the Jews wouldn't put themselves under the Mosaic law

[Minimalist]

But why would the Jews subject themselves to such a rigorous law if they knew it was a myth?

An interesting point and one which erroneously derives from the idea that the jews were somehow special. They weren't. In fact, before they were "jews" they were just average Canaanites but the laws they had lived under in that culture derived from ancient sources.

The Code of Hummurabi dates back to the Middle Bronze Age c 1750 BC. There is evidence that even it was a derivation of earlier law codes.

Check out a few examples.

http://eawc.evansville.edu/anthology/hammurabi.htm

So you must ask the question, did people willingly subject themselves to this law or, did the guys with spears impose it? I think you'll find that throughout much of history the answer is the latter.