In the Disney+ Streaming TV Series, Loki, viewers are introduced to a new organization called the TVA (Time Variance Authority). It is first purposed that that the TVA has created/converged one primary "sacred" timeline and that their agents are dispatched whenever they detect a "nexis event", which is generally a new branch off of the prime timeline. It was also initially purposed that there are three "Time Keepers" in charge of the TVA and the reasons for either "pruning" remaining variants and/or reseting new branch offs is due to this idea that of keeping massive multiuniversal war from occuring...
Viewers eventually learn however that there are not three "Time Keepers", but a man who is refered to as "He Who Remains", but the idea of using the TVA by not allowing a huge multi-verse war is still the goal, as this seemingly happened before, until at some point "He Who Remains" was able to stop a war with his own counterparts and he created the TVA as a result.
So my question is, in regards to the bigger MCU, did the TVA (presumably under the rule of He Who Remians) exist before the events of either Endgame or Infinity War?
Some context for why I am asking the question:
I'm trying to figure out a couple of things, first and foremost what really caused "He Who Remains" to be able to be set free? Was it simply these two Lokis coming into contact or does it specifically go back to the Snap or the Blip? Do the events of the main MCU prior to Loki in anyway play a role in Loki outside of the Tom Hiddleston's alternate? Was what happened with "He Who Remains" intentional on his part? Did he set-up or allow many of the events with Thanos in the MCU or not? And if I can figure this out, I may be able to add something to other questions on Movie & TV Stack Exchange, such as the question about multiple Thanos.