It seems like the mind is created by the brain just as a song is created by an instrument, or an mp3 player. Every time the file is played, the song pops back into existence. Then it goes away. Then comes back.
Our consciousness does the same. A particular state of mind pops into existence in response to certain sensory information and encoded memories. Unlike the mp3, our mental experience evolves with each iteration, expressing growth and continuity, but the underlying nature of the mind and the song is the same: both are patterns, information encoded by physical things. They depend on, yet transcend, the physical. They do not exist apart from the physical, but they are not themselves physical things.
So maybe, given enough time and possibly, our minds pop back into existence every so often, created by different physical bodies in different parts of the universe. And maybe, that is what our daily experience already is--an amalgamation of mental states that are some part unique, never to happen again, and some part universal, repeating themselves countless times throughout the history of life.