Loki comes to Earth through the Tesseract and steals it. At the end, Thor takes Loki and the Tesseract back to Asgard.
When the heist goes wrong, the Tesseract lands at the 2012 Loki's feet. He grabs it and escapes through a portal.
Endgame gives the 2012 Loki a second chance at the cube and lets him escape. That version of Loki is the one picked up later in the Loki TV series (2021).