Intentionally delay starting staffs to avoid lots of rests during intro solo?

[Stig Brautaset]

Hello! I am trying to create a score for a song that has an 8 bar solo
at the beginning. I would like to avoid having staffs for all the other
instruments showing rests, so I'm wondering if it's possible to get
Lilypond to hide the staffs until those voices come in.

I'm hoping it's possible because I noticed that if one instrument has
more measures then its staff will be longer, see e.g. below snippet and
the attached image.

\version "2.19.82"
<<
  \new Staff { a1 b c d }
  \new Staff { r1 b c d e }
>>

Is there a way to get that effect at the *start* of the score as well,
instead of staffs containing nothing but rests?

PS: I'm a beginner both with reading/writing music and Lilypond so feel
free to let me know if this is simply Not Done, especially if you have
suggestions of What To Do Instead. :-)

Regards,

Stig