Reread it again. I don't think there were hints for a time loop except Sakura knowing how to shoot Anzu's gun.
Sakura was called "Pawn of the False Gods" in the dream chapters by one of the false gods that replaced the Count (Ch 12)
In the same chapter, Prez finds out from that same false god that Sakura made that loop wish and why she herself can't die but she will never remember this because she died (with a smile) right after knowing.
Anzu never actually told Sakura the method to shoot her gun, she was in the middle of saying how, but was interrupted by Prez (Ch 15)