How many timelines are there? Or is there just a single timeline and the act of sending this event back in time has always existed, the timelines conjoined at some quantum level.
It feels paradoxical either way to me, but maybe the multiverse is cool with there being universes that are paradoxical.
Perhaps there's a dimension beyond time, and just as information changes in space across time, the entirety of our timeline changes within this upper dimension. The timeline that we once thought was straight and obvious turns out to be wiggling around and looping through itself in this "time of times".