YOU not being able to see how it is possible doesn't mean it isn't possible. Many Christians are TE.
Genesis is not disregarded. Genesis is obviously relevant to TE as we still think God is creator. Genesis does not have to be read literally (which really is for another thread), and has no always been treated as literal. Augustine for example took a symbolic interpretation. Now, regarding one's salvation is an entirely different subject, one I don't think is tenable if you take the position of saying no literal sense means no salvation, but again that is nor here or there.
Well honestly you are wrong. "Create" doesn't mean special creation, though. In fact, "creation" doesn't even have to mean that at all.