How does one sin? By going against something which is prescribed by a cultural construction such as a religion or society. So yes, by that definition you would have been able to "sin" in any social construct with rules. These obviously predate the bible. I might be a good idea to go repost on /r/AskAnthropology for more information on "sinning" in the earliest human societies.

To sin against those rules set forward by the bible, that naturally doesn't predate the bible.