Warning! Serious spoilers here! The MC is not actually Oohashi Rei, she only thinks she is. The original Rei is basically a god that administers humanity, but she is going to try and kill everyone very soon, because her love for Claire is wearing off. Because of that, an AI that Claire created in the first Timeloop made a bunch of copies of Rei in an attempt to ceate a replacement administrator. The MC is the best of this copies and as such was put in this place at the star of the timeloop. This is also why some Rei look-a-likes will appear in the future. They are failed copies of the OG Rei that were given a place in the world.
What the heck? That sounds really bad. Like someone wrote a bad fanfic. What they were thinking?