Vertically centering a title page

There are two small bugs in your code.

First, if you want the \vspace to work at the beginning or end of a page, you should use the starred version (\vspace*).

This would work, but \maketitle is a pretty complicated macro, and if used like in your example, it just puts the title at the second page. You can use the titlepage environment, which gives you much more command over how the title page looks like — including the spacing. For example, you could use the following code:

\documentclass{article}
\setlength{\pdfpagewidth}{88.184mm}
\setlength{\pdfpageheight}{113.854mm}

\usepackage[margin=0.5cm, paperwidth=88.184mm, paperheight=113.854mm]{geometry}

\begin{document}
  \begin{titlepage}
    \vspace*{\fill}
    \begin{center}
      {Huge [Vertically centering a title page]}\\[0.5cm]
      {Large [[author}\\[0.4cm]
      [[date]]
    \end{center}
    \vspace*{\fill}
  \end{titlepage}

  [[text]]
\end{document}