Removing the first empty line

The first empty staff can also be removed from the score by setting the VerticalAxisGroup property remove-first. 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
  }
>>

\paper { tagline = ##f }