Is there a way to perform "if" check only once instead of every iteration in a loop?

Detach the first conditional.

\documentclass{article}

\newcount\zNonZero

\def\zLoop#1{%
  \zNonZero=1
  \zLoopStart{#1}%
  \zLoopLoop{#1}%
}
\def\zLoopStart#1{%
  \ifnum#1<1 % HOW TO CHECK THIS ONLY ONCE?
    \zNonZero=0
  \fi
}
\def\zLoopLoop#1{%
  \ifnum#1<5
    #1...(\the\zNonZero)\par
    \zNonZero=1
    \expandafter\zLoopLoop\expandafter{\the\numexpr#1+1\expandafter\relax\expandafter}%
  \fi
}

\setlength{\parindent}{0pt}

\begin{document}

\zLoop{0}

\end{document}

Note the two more \expandafter tokens so the entire conditional is removed before the loop is restarted.

This possibly doesn't qualify, but I'll mention it anyway.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn

\NewExpandableDocumentCommand{\zLoop}{m}
 {
  \bp_zloop:n { #1 }
 }
\cs_new:Nn \bp_zloop:n
 {
  \int_compare:nT { #1 < 5 }
   {
    #1...(\int_eval:n { \int_min:nn { #1 } { 1 } })\par
    \bp_zloop:f { \int_eval:n { #1 + 1 } }
   }
 }
\cs_generate_variant:Nn \bp_zloop:n { f }

\ExplSyntaxOff

\begin{document}

\zLoop{0}

\end{document}

\documentclass{article}    
\begin{document}
    \parindent0pt
    \newcount\zNonZero
    \newif\ifCheck \Checktrue
    \def\zLoop#1{%
        \zNonZero1
        \ifCheck\ifnum#1<1 \zNonZero0 \fi\Checkfalse\fi
        \ifnum#1<5
        #1...(\the\zNonZero)\newline
        \expandafter\zLoop\expandafter{\the\numexpr#1+1\relax}
        \fi
      \Checktrue
    }
    \zLoop{0}
\end{document}