WI: James Bond Films Came Out in Order of the Books?

Dr.No was the first James Bond book to be turned into a film, but it is the sixth James Bond book that Ian Fleming wrote. I don't know much about the history of the film franchise, but what if instead of Dr.No, Casino Royale, the first James Bond book, was turned into the first James Bond film? not only that, but let's also say that all future films released would follow with the order the books were published. How would things be different? Would Sean Connery still be cast as Bond?
 
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