A fine argument, but I think you missed one consideration: What if consciousness is, has always been, and will always be present, but what humans experience as consciousness only occurs when it gains something to focus on?
I would argue that the "Mind" as you call it is nothing more than consciousness, which doesn't have any computing power, but instead merely allows a person to look at the "logs" of the brain, which does have a great deal of computing power, and to experience reality through them.
Humans are born as a result of matter interacting with other matter, so at some point during the formation of the brain, either consciousness(a non-physical entity) was created during the(purely physical) process of human development as a result of the interaction of matter, which we both likely find implausible, or it gained something to focus on, some "logs" to read at some point during the process.
If the brain can somehow bind to a consciousness or create one, why can't a computer that works on different principles? Would you say that a fully accurate, particle-level simulation of the brain is conscious? Or are you claiming that there something unique to organic matter that allows it to be called a mind rather than a computer?