If there is one thing that people would have to understand about Loki, it is that he is smart beyond his tricks and schemes to be able to pull those things off. He proved this in Episode 2 of his own canon series titled "The Variant" through his theory of where the hiding place of the Loki Variant might be. It may sound confusing at first but if you put yourself into how he thinks, you'd easily recognize his genius.
In Loki Episode 2, The Variant, Loki showed off his wits by proving his theory of where the Loki Variant is possibly hiding in their pursuit against the mischievous scamp that has been killing off agents of the Time Variance Authority.
Loki approached the librarian in hopes of knowing more about the Time-Keepers, the origins of the TVA, the start of time, and its end. All these were deemed classified and the only thing which isn't classified was given to him was about the Destruction of Asgard where Loki realizes that his home is going to be obliterated by a level seven apocalyptic event caused by the prophecy of Ragnarok.
This gave Loki an idea of where the variant could possibly be hiding, in an apocalyptic event where there is no variance detected. In his theory, Loki explains that when a timeline is about to be totally destroyed by some apocalyptic event wiping out all in existence in such place and time, there would be no branches anymore as the mainline where it comes from is already cut off.
Loki explains to Mobius in a hilarious depiction using the salad he was eating that when an apocalypse is bound to happen, whatever possible branch is to be created near the end would prevent it from having any variance or some temporal aura detected as the timeline would be cut off by the said event.
To simplify it, picture this, the Loki variant is hiding at the end of a tree branch, the tree branch remains attached to the tree and the tree is the Sacred Timeline. Once the branch is completely off the tree and falls off, it could not produce or grow any more branches. Whatever is done on the branch about to fall off, it would not stop it from falling, hence, the apocalypse still happens and the variant could not be detected as they are focusing on the branch falling off of the tree rather than its surroundings.
Loki proved this theory as he and Mobius went to Pompeii and Loki announced to the village that all of them would die, even freeing the goats. In the detector of Mobius, there was not branching event determined as it has been perfectly covered by the apocalyptic event.
Later in the episode, Mobius correlated this theory of Loki with the kablooey gum that he got from the child in the premiere. They found the level ten apocalyptic event in 2050 at the Gulf Coast where a hurricane wipes out everyone hiding at Roxxcart.
Loki was right all along; the variant was there. What they did not expect was the plot of the variant who turns out to be Lady Loki, the character of Sophia Di Martino. As the reset charges went off, various branches were detected and the TVA is on their heels trying to stop all of it from reaching the red line.
Loki, in whatever form, is definitely one hell of a genius!
All episodes of Loki Season 1 are available to stream on Disney+.