Hidden subsection 0

Hidden subsection 0

I'd like to have an intro to a section 3 that would be referenced in the text as section 3.0. It should be a hidden subsection (before the first real subsection) that doesn't have a section header nor shows up in the table of contents.
\section{Section 3}
\label{sec:3}

\setcounter{subsection}{-1}
\subsection{ }
\label{sub:3_0}
yada yada
However, then I get a section header with the numbering. And I have tried
\section{Section 3}
\label{sec:3}

\subsection*{}
\label{sub:3_0}
yada yada
However, then my referencing, shown here
\subsection{Section 3.1}
\label{sub:3_1}
yada yada \cref{sub:3_0}.
only gives me section 3 instead of section 3.0.
Anybody know the answer? Also, feel free to comment on my style choice (using .0 section numbers).