In Episode 2, "The Variant", Loki twice talked about "overthrowing the Time Keepers and ruling TVA": the first time when he tricked and cheated (but failed) to persuade Agent Mobius letting him meet the Time Keepers, the second time when convincing Lady Loki (Randy) to cooperate with him. So what makes Loki think about such a strategy?

@ The episode is shown on Disney+ or as per the movie link near the bottom of the article.

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This may be just the spoken words rather than the actual motives and intentions of Loki, but it is assured that that he is thinking seriously about the matter.

Firstly, Loki is worried about his future.

He was sentenced to the death (reset) by the Judge, and has a chance to survive thanks to Mobius' proposal to keep him alive just to help track down the Variant. If he failed to help TVA catch the Variant, there would be no reason for them leave him alive. But after supposedly capturing the Variant, where is the guarantee that he will not be executed, and where will he live, and in what role and position?

The Time Keepers may be great and powerful to the TVA staffs, but Loki must have viewed them as mediocre, since he himself was a God who once ruled over an entire planet. TVA personnel also have no superpowers other than unique weapons and technologies. In fact, many TVA units were easily slaughtered by Randy, and the flaw or loophole in their universally theory has been figured out by Loki himself.

And so, overthrowing the Time Keepers will be the way out for him. Loki must have such thought somehow. But hold on, so far, no one in the universe can predict what is really happening in Loki’s mind.

Secondly, Loki may want to change history.

The current Loki in 2012 has the perfect opportunity to witness the fate of the mainstream Loki with all the loss and pain from the perspective of relatives, ethnics and homeland.

1 year later, in 2013, Loki's goodhearted and strong adoptive mother Frigga died at the hands of Malekith the Dark Elf in "The Dark World".

5 years later, in 2017, Odin - Loki's adoptive father died because of Loki's own sins in the events of "Thor: Ragnarok". Thor lost an eye. Also in this year the planet Asgard was completely destroyed.

Loki's Asgardians have been constantly experiencing traumatic sufferings and even near-extinction.

In Thor: Ragnarok, the entire army loyal to Thor and most of the population of Asgard were killed by Hela in the battle for the throne. Before the planet was destroyed by Surtur, only a portion of the population managed to escape to the ship The Statesman to evacuate, the rest must have all died.

At the beginning of Infinity War, half of the evacuees aboard The Statesman were killed by Thanos and the Black Order, including the mainstream Loki and Heimdall.

Asgard's population was estimated at 50,000 citizens, but after the Endgame, this number dwindled to just under 1,000.

It's certain that Loki does not want such a history to happen, and he want to and has to change it because if he couldn’t, he would have nothing: no relatives, no homeland, no planet, no races … and nowhere to rule. Meanwhile, TVA's “glorious purpose” is to preserve the timeline, keeping the historical status quo as it is.

And in order to change then history, Loki can think of two ways, either wiping out TVA or overthrowing the Time Keepers to rule TVA and control it to his will. Of course, his bright mind may invent some other options.