Max's Time Rewind Mechanic came from her camera.
In the original game, the first time Max uses her powers is when she rewinds back to the moment she took a picture with her old polaroid camera during Mark Jefferson's class. This theory exposits that Max's old Polaroid camera was an Object of Power and she unknowingly bound with it. In Jungian terms, photography is used to capture a specific moment in time that can be revisited and reinterpreted, so it stands the reason that translating the symbolism literally would allow Max to go back to specific fixed points in time and relive them. Whether the camera was always and Object of Power and her binding with it had anything to do with the AWE soon after, or if the AWE imbued it with enough paranatural energy to turn it into an OoP is pure conjecture.Max is a Prime Candidate for the Director position.
She has visions of the astral plane and The Board, she's the survivor of an AWE event, she can use the Hotline (which is one of two OoPs that exist to only be used by Jesse by virtue of her position) and she's a superpowered protagonist who's actions can save or doom countless people. It's kind of a no-brainer that, should the need arise, Max would be able to use the Service Weapon without it killing her. She might even be labeled a potential "heir" to the Bureau in the event that Jesse can no longer act as Director.