Hi there,
the height of the Header Elements ( which are found in Appearance > Elements ) are defined primarily by three things:
1. The Content – the more lines of content the taller it will be.
2. The Top Padding and Bottom Padding.
3. The Offset Site Header Height ( set on the Site Header tab in the header element ).
For all of the pages #3 is identical.
So choices are to edit the Header Element assigned to the Front Page and reduce its top and bottom padding. Other than that you would need to reduce the amount of content…..