I have prepared a \header and I would like to increase the vertical space before my first stave, which also includes chords.

Is that also possible with LilyPond?

The simplest approach would be to include a \markup \vspace #1 command before your score block. You can change the #1 to any value, including values with decimals.

\version "2.18.2"

title = "This"
}

\markup \vspace #1 % change this value accordingly

sample = \relative c'' {
c4
}

\score {
\new Staff \sample
\layout { }
}