CircuiTikZ: Start ground relative to the closest component

Although I suspect this is a kind of XY problem, no, there is no provision (for now) for a tailless ground symbol. It is quite straightforward to define one, though:

\documentclass{article}
\usepackage[RPvoltages]{circuitikz}

\makeatletter
\pgf@circ@declareground{myground}{0.6}{0.4}{
    \pgfsetlinewidth{\ctikzvalof{monopoles/ground/thickness}\pgfstartlinewidth}
    \pgfpathmoveto{\pgfpoint{-.6\pgf@circ@res@step}{0pt}}
    \pgfpathlineto{\pgfpoint{.6\pgf@circ@res@step}{0pt}}
    \pgfpathmoveto{\pgfpoint{-.4\pgf@circ@res@step}{-0.2\pgf@circ@res@step}}
    \pgfpathlineto{\pgfpoint{.4\pgf@circ@res@step}{-0.2\pgf@circ@res@step}}
    \pgfpathmoveto{\pgfpoint{-.25\pgf@circ@res@step}{-0.4\pgf@circ@res@step}}
    \pgfpathlineto{\pgfpoint{.25\pgf@circ@res@step}{-0.4\pgf@circ@res@step}}
    \pgfusepath{draw}
}
\makeatother

\begin{document}
    \begin{circuitikz}
        \draw (0,0) node[ground]{} to [C, *-*] (0,2);
        \node[xshift=1.75cm](0,0){$ \leftarrow $ Start ground here};
        \draw (4,0) node[myground]{} to [C, *-*] (4,2);
    \end{circuitikz}
\end{document}

Note that I also simplified out your zero-length short.

You can just shift the ground up a little, if you don't mind overlapping the tail.

\documentclass{standalone}
\usepackage{tikz}
\usepackage{circuitikz}

\newlength{\kludge}

\begin{document}
    \begin{circuitikz}
        \kludge=\ctikzvalof{monopoles/ground/width}\csname pgf@circ@Rlen\endcsname
        \draw (0,0) node[ground,yshift=1.2\kludge]{} to [C,*-*] (0,2);
        \node[right=0.5\kludge]{$ \leftarrow $ Start ground here};
    \end{circuitikz}
\end{document}