How to add a logo at the top center of the titlepage in beamer and optimize the template

Question

I am making a presentation with beamer using the Madrid theme. I am trying to add an institutional logo only at the top center of the title page. What is the most effective way to do it?

I have done in the following way:

\documentclass[aspectratio=43]{beamer}  
%------------------------------------
\mode<presentation>{
\usetheme{Madrid}
}
\setbeamercolor{section in head/foot}{fg=white,bg=black}           % https://tex.stackexchange.com/a/326553/114006
\makeatletter
\setbeamertemplate{headline}{%
    \begin{beamercolorbox}[ht=2.25ex,dp=3.75ex]{section in head/foot}
        \insertnavigation{\paperwidth}
    \end{beamercolorbox}%
}%
\makeatother
%------------------------------------
\title{Presentation Title}
\titlegraphic{\includegraphics[width=1cm]{example-image}}
\author{Presenter Name} 
\date{August, 2021} 
\logo{\includegraphics[height=0.5cm,keepaspectratio]{example-image}}

\begin{document}
{
\setbeamercolor{page number in head/foot}{fg=date in head/foot.bg}          % https://tex.stackexchange.com/a/412733/114006
\begin{frame}[noframenumbering, plain]
\titlepage
\end{frame}
}
\section{Section 1} 
\begin{frame}
\frametitle{Section One}
Sed iaculis dapibus gravida.
\end{frame}
\setbeamercolor{page number in head/foot}{fg=date in head/foot.bg}
% \bulletoff\section*{}
\begin{frame}[noframenumbering]
\Huge\centerline{Thank You.} 
\huge\centerline{Any Question?}
\end{frame}

\end{document}

Besides the logo issue, I wish to get suggestions to optimize the overall template code. At what places can it be improved?