Removing the first empty line

To remove the first empty staff from a score, set the remove-first property of the VerticalAxisGroup grob to #t. This can be done globally inside the \layout block or locally inside the specific staff that should be removed. In the latter case, you have to specify the context (Staff applies only to the current staff) in front of the property.

The lower staff of the second staff group is not removed, because the setting applies only to the specific staff inside of which it is written.

\version "2.24"

\layout {
  \context { 
    \Staff \RemoveEmptyStaves 
    % To use the setting globally, uncomment the following line:
    % \override VerticalAxisGroup.remove-first = ##t
  }
}
\new StaffGroup <<
  \new Staff \relative c' {
    e4 f g a \break
    c1
  }
  \new Staff {
    % To use the setting globally, comment this line,
    % uncomment the line in the \layout block above
    \override Staff.VerticalAxisGroup.remove-first = ##t
    R1 \break
    R
  }
>>

\new StaffGroup <<
  \new Staff \relative c' {
    e4 f g a \break
    c1
  }
  \new Staff {
    R1 \break
    R
  }
>>