1

This MWE does not produce a zero margin page. The word "Test" is shifted about 0.5cm from the left.

\documentclass[10pt,letter,article]{memoir}

\usepackage{geometry}

\geometry{left=0in, right=0in, top=0in, bottom=0in}

\begin{document}

Test

\end{document}
1

The remaining margin in your test file is due to the indentation of the first paragraph. The following produces what you want:

\documentclass[10pt,letter,article]{memoir}

\usepackage{geometry}

\geometry{left=0in, right=0in, top=0in, bottom=0in}

\begin{document}
\noindent % no indent of the first line in this paragraph
Test

\end{document}

If you don't want the indent of each first line of a paragraph, you might reduce the indentation to 0pt with \setlength{\parindent}{0pt}

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