If you want exactly one point of space above the title, then you need some deeper control on spacing.
With \vspace*{1pt}\begin{center} the standard space above center is not removed because it's preceded by something that must not be removed at a page break (the start of a document counts as a page break). Thus you get the total of 1pt plus the \topsep.
On the other hand, you probably don't actually want center, but only centering the title.
\documentclass{article}
\usepackage{showframe}
\begin{document}
\vspace*{1pt}% the space you want
\vspace{-\topskip}% remove the topskip
\begingroup\centering\Huge
Test text\par
\endgroup
\addvspace{\topsep}% or what you need
Some other text follows.
\end{document}
Note that you need something more than just \vspace*{1pt}.

\begin{center}introduces vertical padding which is however ignored at the start of a page. – campa Feb 08 '24 at 11:49\Hugeis a switch and does not take an argument. Use\Huge Test text.or{\Huge Test text.}if you want to restrict the change to a certain group. – samcarter_is_at_topanswers.xyz Feb 08 '24 at 11:54\vspace*{1pt}into thecenterenvironment. – samcarter_is_at_topanswers.xyz Feb 08 '24 at 11:57