From what you translated though it appears the BEE possibility already existed and co-existed alongside Blazblue and the other possible worlds until something occur to only make the Blazblue timeline the only possible world. CF is the result of the other timelines being destroyed with the result of whatever happens in the CF timeline being the only possibility and result allow to influence the world while the other worlds are treated as if they didn't exist at all. Naoto being sent to the CF timeline is to find someway to undo whatever caused the process of the world possibilities being destroyed while using the CF timeline as a means to reboot those possibilities in order for his world to come back.