Almost half a century after Close Encounters of the Third Kind, Steven Spielberg seeks to get us all up on that starship with the big-hearted Disclosure Day.

This image released by Universal Pictures shows Colman Domingo, from left, Tommy Martinez, Emily Blunt and Josh O’Connor in a scene from “Disclosure Day.”

Disclosure Day tells the story of a U.S.-government led conspiracy to keep the existence of intelligent alien life a secret, and how those plans are upended by small determined group committed to “dis...