You move all the \author, \title etc into the preamble. Beamer will automatically use this information at the start of the document to create the meta data for the pdf. If you only use them after the start of the document, that's too late for beamer.
\documentclass[presentation]{beamer}
%\let\Tiny\tiny
%\usepackage{hyperref}
\usetheme{Berkeley}
\author[A,B,C]{A\inst{1} \and B\inst{2} \and C\inst{2}}
\renewcommand{\thefootnote}{$\aleph$}
\title[Cross]{\large Experimental Studies %
\thanks{\scriptsize Project supported by foundation: Supported by the National Nature Science Foundation}}
% Old style
%\author[A,B,C]{A$^1$,
%B$^1$
%and C$^2$}
\institute[Fluid Mechanics]{$^1$Department of Mechanics & Engineering Science\
$^2$College of Science}
\date[The second presentation, 2013]{The second presentation, 2013}
%\logo{\includegraphics[height=16pt]{picture/Fudanlog.PNG}}
\date[\initclock\tdtime]{\today}
\begin{document}
\begin{frame}
\titlepage
\end{frame}
\section{A section}
\subsection{A subsection}
\begin{frame}
\frametitle{Frame title1}
\framesubtitle{frame subtitle1}
Some text s
\end{frame}
\end{document}
\begin{document}just before the first\begin{frame}... – Paul Gaborit Jun 15 '22 at 05:40