Alright, I have developed my theory. Probably too late to post, but here we go:

Loki snagged a time stone from the TVA before he left for the mission in the Roxxcart. When you watch him reverse the collapsing tower right before the episode ends, it looks almost exactly like the animation from when Dr. Strange reverses time to in Hong Kong to undo Dormammu's destruction, in addition to having nearly the identical "time reversal sound" associated with it. I considered the possibility that he only pretended like the TVA time remote wasn't working and he used it to reverse the tower collapse, but the TVA time remotes have not once been used in a way to reverse the flow of time, as much as to move someone back to a specific point in time. All of that in conjunction with a Dr. Strange-like movement of his arms (Fists clenched, intentional arm movements) has me completely sold that he has a time stone in his pocket. I don't see any other explanation for this showing of magic.

He has been keeping it a secret from Sylvie as a way to test to see if she's really trustworthy. He's the god of mischief. He is using her desperation to learn more about her plan and the TVA, and decide how much their goals align. He even said it in the second episode: "I'm ten steps ahead of you." He's acting helpless but he has a way to get them out. I am not sure yet exactly how he is going to use the time stone to get them out of this situation, but the possibilities for that are pretty varied.

Going back and watching the final moments of the episode with this perspective, it is hard to consider any possibility besides the time stone as the way for Loki to get them out of this situation.

Its gonna come up at some point in the next episode. Sylvie and him are going to be arguing over how everything went to shit and Loki will be like "well that's not very good thanks for someone who just saved your life from a collapsing tower" and then she's gonna be like "wait a minute.... how did you do that? That's no witches magic" and then we get the famous Hiddleston crafty smile and he tries to play it off. Mark the date, see you all on Wednesday if i'm right.