With the preamble that I built from the answer on \section with empty title. Show number next to first paragraph, I use \section{} and related with empty title, which will mark the first paragraph of the section with a number. This is perfect for my use case, however:
How do I exclude the sections with empty title from the TOC?
What I've got so far is this:
\documentclass{report}
\usepackage[a4paper, margin=1.3in]{geometry}
\usepackage{etoolbox}
\usepackage[explicit]{titlesec}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Set section numbers in the margin and center the chapter headings
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setcounter{secnumdepth}{5}
\renewcommand\thesection{\arabic{section}}
% this length controls the hanging indent for titles
% change the value according to your needs
\newlength\titleindent
\setlength\titleindent{1.35cm}
\titleformat{\chapter}[block]
{\normalfont\huge\bfseries\center}{}{0pt}{\hspace*{-\titleindent}#1}
\titleformat{\section}
{\normalfont\Large\bfseries}
{\llap{\parbox[t]{\titleindent}{\thesection\hfill}}}{0em}
{\if\detokenize{#1}\relax\relax
{\Large\bfseries\vspace*{-\dimexpr2.3ex+0.5\baselineskip\relax}}
\else#1
\fi
}
\titleformat{\subsection}
{\normalfont\large}{\llap{\parbox[t]{\titleindent}{\thesubsection\hfill}}}
{0em}
{\if\detokenize{#1}\relax\relax
{\Large\bfseries\vspace*{-\dimexpr1.5ex+0.5\baselineskip\relax}}
\else\bfseries#1
\fi
}
\titleformat{\subsubsection}
{\normalfont\normalsize}{\llap{\parbox[t]{\titleindent}{\thesubsubsection}}}
{0em}
{\if\detokenize{#1}\relax\relax
{\Large\bfseries\vspace*{-\dimexpr1.5ex+0.5\baselineskip\relax}}
\else\bfseries#1
\fi
}
\titleformat{\paragraph}[runin]
{\normalfont\large}{\llap{\parbox{\titleindent}{\theparagraph\hfill}}}{0em}{}
\titleformat{\subparagraph}[runin]
{\normalfont\normalsize}{\llap{\parbox{\titleindent}{\theparagraph\hfill}}}{0em}{}
\titlespacing*{\chapter}{0pt}{0pt}{20pt}
\titlespacing*{\section}
{0pt}{3.5ex}{2.3ex}
\titlespacing*{\subsection}
{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\titlespacing*{\subsubsection}{0pt}{3.25ex}{1.5ex}
\titlespacing*{\paragraph}{0pt}{3.25ex plus 1ex minus .2ex}{0em}
\titlespacing*{\subparagraph}{0pt}{3.25ex plus 1ex minus .2ex}{0em}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Make chapters show up in TOC and NOT reset the section counters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setcounter{chapter}{0}
\newcommand{\mychapter}[1]{
\chapter*{#1}
\addcontentsline{toc}{chapter}{#1}
}
\begin{document}
\tableofcontents
\cleardoublepage
\mychapter{INITIAL CLAUSES}
\section{A Section title}
\subsection{A subsection with a title}
Some text
\subsection{} This subsection has no title, so the numbers are displayed next to this text instead.
\subsection{} These subsections should not be included in the TOC
\end{document}


