Is there a way to solve that?

Thanks a lot!
Yes, it's possible; the section number is typeset by the macro \@seccntformat and it's just a matter of giving it a suitable redefinition: typeset the number in a fixed width box.
\documentclass{article}
\usepackage{indentfirst}
\usepackage{lipsum}
\makeatletter
\renewcommand{\@seccntformat}[1]{%
\protect\makebox[\parindent][l]{\csname the#1\endcsname}%
}
\makeatother
\setlength\parindent{2.5pc}
\begin{document}
\section{Lorem ipsum}
\subsection{Aliquam vestibulum}
\lipsum[2]
\subsubsection{Aliquam vestibulum}
\lipsum[2]
\end{document}

When minitoc is loaded (which I don't recommend, I find it distracting and not really useful), a bizarre thing happens: the package unfortunately redefines a key macro without using \@seccntformat, which is utterly wrong. You can patch it, though, restoring the correct behavior.
\documentclass{article}
\usepackage{indentfirst}
\usepackage{minitoc}
\usepackage{etoolbox} % for \patchcmd
\usepackage{lipsum}
\makeatletter
\renewcommand{\@seccntformat}[1]{%
\protect\makebox[2.5pc][l]{\csname the#1\endcsname}%
}
% patch the wrong definition of `\stc@sect`
\patchcmd{\stc@sect}
{\edef\@svsec{\csname the#1\endcsname\hskip1em}}
{\protected@edef\@svsec{\@seccntformat{#1}\relax}}
{}{}
\makeatother
\setlength\parindent{2.5pc}
\begin{document}
\section{Lorem ipsum}
\subsection{Aliquam vestibulum}
\lipsum[2]
\subsubsection{Aliquam vestibulum}
\lipsum[2]
\end{document}
minitocis badly written, unfortunately. I added a patch. – egreg Apr 04 '14 at 16:34minitoc's also (i think) the largest single latex package on ctan. it incorporates a lengthy essay (with maps and flags included) about (i suppose) tocs. i'd sort of vaguely thought of negotiating "inheriting" it from drucbert, but i've never quite had the necessary effort available. – wasteofspace Apr 04 '14 at 16:40minitoc's features can be replicated usingtitletoc– cmhughes Apr 04 '14 at 17:20