Out of Time

Out of Time is a main quest in Fallout 4.

Detailed walkthrough
Essentially retrace the path the player character took to get to the vault to get back to the Sanctuary Hills neighborhood and house. Codsworth will be near the player character's home. The interaction with Codsworth serves as the dialogue tutorial.

Explore the neighborhood by following Codsworth who is searching for signs of life. This will lead to combat with Bloatflies and radroaches. When two battles are done, Codsworth will suggest the Sole Survivor go to Concord to continue the search for Shaun.

The road to Concord leads south out of Sanctuary Hills across the bridge. On the way, there is a Red Rocket truck stop where a Dog can be found that is willing to accompany the Sole Survivor as a companion. Upon entering Concord this quest will complete and the next quest When Freedom Calls will begin.