This question has be touted and asked throughout the history of Mankind! Don't get hung up in the word "Torah", it simply means learning, teaching, instructions and all that that entails. All and any of the Writings is Torah.
So with that in mind when was Torah first pasted down to us? I give you a hint before we were made from the dust of the earth. YHVH (Yahweh) began with Yeshua, Then came everything else! The first was establishing the days; even and morning day one.
Now it says that Yahweh walked with Adam in the cool the day, somewhere in the mix or before that. But we know that Eve (Havah) was bot separated into a separate person just yet. Yahweh said don't eat of the Tree of knowledge of good and evil! That was more torah and the second rule. First was 6 days of work, 1 day of rest Sabbath. Second was don't eat of the one tree.
I'm sure most of you know, be fruitful and multiply. Also is what qualifies as Torah? Remember that Constantine was responsible along with the Catholic fathers of setting what was in the "Bible"; not Israel or Jews.
So what is Torah?