I'm not sure I'd say Meursault doesn't exist until the second part of the book. This book isn't your typical "finding enlightenment" kind of epiphany. Meursault has always found his essence by experience: no matter what the situation is. That's why he seems so indifferent all the time - he just accepts the reality which he finds himself in. He still feels like a stranger in prison - perhaps even more so than when he was free. So, if he found more of his essence in Book Two, it is his increased isolation from society. While in prison, he even makes a point that one day on the outside gives him enough to think about for years in prison.
In Book II, he doesn't find his essence, but I guess you could say he was further convinced that his idea of absurdity and his concept of his essence had been confirmed. He sees death as the equalizer of all, which makes life absurd and meaningless and he gains some solace from this.
He does miss his freedom; and maybe this is more essential in terms of his essence. He still feels like an outcast and has come to terms with this. But he certainly would prefer to be a free outcast than an imprisoned one. He is and has always been mentally free, but realizes he that the corresponding physical freedom is something he'll miss.