\version "2.22.1"

#(define (stencil-without-Y-extent stil)
   (ly:make-stencil (ly:stencil-expr stil)
                    (ly:stencil-extent stil X)
                    empty-interval))

#(define (down-hanging-stencil stil)
   (ly:stencil-translate-axis stil
                              (- (cdr (ly:stencil-extent stil Y)))
                              Y))

\layout {
  \context {
    \Score
    \consists Time_signature_engraver
    \override TimeSignature.style = #'numbered
    \override TimeSignature.font-size = 6
    \override TimeSignature.Y-offset = 0
    \override TimeSignature.stencil =
    #(grob-transformer
      'stencil
      (lambda (grob default)
        (stencil-without-Y-extent
         (down-hanging-stencil (ly:stencil-scale default 1 3)))))
  }
  \hide Staff.TimeSignature
}

<<
  \new Staff { c'1 \time 3/4 c'2. }
  \new Staff { c'4 c' c' c' c' }
  \new Staff { c'2 c' c'2. }
>>