Yes, it is possible to remove the header bar of an embedded story map to maximize its view within a story map. Refer to FAQ: Is it possible to embed multiple web maps in a single web app? for more information on story map templates that can be embedded within another story map.
To remove the header bar of an embedded story map, add the &embed URL parameter at the end of the story map URL when configuring it to be embedded within another story map. For detailed steps on removing the header bar, refer to the 'Minimize before embedding' and 'How to embed a Story Map' sections in ArcGIS Blog: Embed a Story Map within a Story Map.