Walkthrough: After defeating your final Island Trial on Akala Island, Professor Kukui will suggest heading to the Dimensional Research Lab in Heahea City. As you arrive, Professor Kukui will introduce you to his wife, Burnet, who is a researcher at that facility. She will mention how she is researching Ultra Wormholes, the same that Ultra Beasts, including Cosmog, travel through.
After getting acquainted, you will be tasked with talking with Lillie before proceeding in your journey. Lillie will tell you how Cosmog teleported her from where she use to be, being found by Professor Kukui and his wife. The two were then kind enough to let Lillie live with them in their loft. Once you've finished speaking with everyone, you will continue onward to Diglett Tunnel just south of Heahea City. As you leave the Dimensional Research Lab, you will see a small Wormhole appear (but not open) within the sky above.