All letters in uppercase, but the first letter bigger than the other ones

You are most likely referring to small caps:

\textsc{First Letter}

or

{\scshape First Letter}

One can adapt expl3 code that egreg published in TUGBoat recently (TUGboat, Volume 39 (2018), No. 1, pg.55). Like Werner's solution using small caps, this solution assumes that the leading letters are entered as capitals. However, you can choose the size (and by extension other attributes)

\documentclass[11pt]{article}
\usepackage{xparse}
\usepackage{expl3}

\ExplSyntaxOn
\NewDocumentCommand{\biglittlecap}{m}
{
\sheljohn_biglittecap:nn { #1 }
}
\tl_new:N \l__sheljohn_biglittecap_input_tl
\cs_new_protected:Npn \sheljohn_biglittecap:nn #1
{
% store the string in a variable   
\tl_set:Nn \l__sheljohn_biglittecap_input_tl { #1 }
\regex_replace_all:nnN
% search a capital letter (or more)
{ ([A-Z]+ | \cC.\{?[A-Z]+\}?) }
% replace the match with \huge{match}
{ \cB\{\c{huge}\1\cE\} }   % <=== could use large, Large (or some other command...)
\l__sheljohn_biglittecap_input_tl
\tl_use:N \MakeUppercase{\l__sheljohn_biglittecap_input_tl}
}
\ExplSyntaxOff

\begin{document}

\biglittlecap{\`Once \r{U}pon a Time}

\end{document}