As indicated in the comments TikZ does not necessarily add a lot of time to the compilation. However, just for the sake of an alternative here a picture mode version with the built-in commands \circle (open circle) and \circle* (filled circle).
You can create a new command that takes as argument the diameter of the circle. In the MWE below this argument is optional with a default of 2mm. The command draws a filled red circle with an open black circle (with thick lines). Both circles are drawn at the coordinate (0,0) which means they are drawn overlapped.
The more difficult issue is how to position the circle vertically and horizontally centered for different sizes. To do this the picture environment is specified with size (diameter,diameter) (i.e., (#1,#1)) and the lower left corner at (-0.5 * diameter,-1). To calculate -0.5 * diameter the argument can be stored in a length (here called \argwidth) which allows for fractional values.
\documentclass{article}
\usepackage{xcolor}
\newlength{\argwidth}
\newcommand{\circdiam}[1][2]{%
\thicklines%
\setlength{\unitlength}{1mm}%
\setlength{\argwidth}{#1mm}%
\begin{picture}(#1,#1)(-0.5\argwidth,-1)%
\put(0,0){\color{red}\circle*{#1}}%
\put(0,0){\circle{#1}}%
\end{picture}%
}
\begin{document}
$0 < \circdiam[1] < \circdiam < \circdiam[5] < 10$
\end{document}

Note that for bigger sizes the picture reserves a bit too much space at the top. As a workaround you can smash it:
\begin{document}
See the following equation, that has a sentence in front
that spans the whole line, and the equation
$0 < \circdiam[1] < \circdiam < \smash{\circdiam[5]} < 10$
is embedded in a sentence to check the spacing around it.
We show that $0<10$.
\end{document}

tikz consumes a lot of compilation time, this is usually be cause of very complicated drawings or plots and not something as simple as\tikz\draw[overlay,fill=red] (0,2bp) circle (1bp);– daleif Dec 13 '22 at 08:06\usepackage{tikz}usually increases compilation time by a number of seconds because all of the files that are loaded, so I understand the reasoning of the OP not to load TikZ just for a colored circle. – Marijn Dec 13 '22 at 10:35\usepackage{tikz}makes the compilation time 0.1s longer, that is it. – daleif Dec 13 '22 at 10:53