The Omega dying before it is killed is inconsistent with the rest of the film. Admittedly the Omega is different but if the death of the Omega allows it to throw its own consciousness back in time in the same way that the Alphas and Cage and Rita did (which would be consistent), then it would know how it died. The obvious requirement is then to prevent the events that led to its death. So Cage must not go onto that beach tomorrow morning. Or at least not go to Paris in the middle of the night. So the Omega relocates itself and ceases effective resistance while marshalling sufficient of its forces to defend or attack elsewhere. Cage isn't shanghied and he, Rita and J squad don't go to the Louvre. The Omega isn't killed. The Russians and Chinese push forward in the East, the USA, UK and Canada land in France unopposed, push forward carelessly thinking their enemy is finished, and then run into a massive ambush later and are wiped out?
This is consistent with what is shown in the film, allows for endless sequels if it does well, and has only taken me one showing and 2 1/2 days to think of so I'm sure someone else has thought of it before me.