You mentioned in your other comment you did this. Well, here is my attempt.
Just to be clear. In Mathematica Style[OverHat["X"],... is done in text mode. While MaTeX works in Math mode. So you can not expect same output as is. To use MaTeX in textmode, need to use \text command in Latex which allows one to insert text in math mode.
To use Matex to generate the same output:
To set font to Arial, need to use lualatex as not possible with pdflatex. So need to tell MaTeX to use lualatex
Needs["MaTeX`"]
ConfigureMaTeX["pdfLaTeX"->"C:\\Users\\Owner\\AppData\\Local\\Programs\\MiKTeX\\miktex\\bin\\x64\\lualatex.exe"];
SetOptions[MaTeX,"Preamble"->{"\\usepackage{fontspec}\\setmainfont{Arial}\\usepackage{amsmath}"}];
And now, to use 20pt in Latex also
MaTeX["\\text{\\fontsize{20pt}{16pt}\\selectfont \\^{X}}"]
Same as Mathematica. Screen shot (but the hat I used is a little bit different size).

All under windows 10.
MaTeX works in math mode. So had to use \text in the above. Can not use text directly inside MaTeX call.
If you want wider hat in textmode, you can try this
Needs["MaTeX`"]
ConfigureMaTeX["pdfLaTeX"->"C:\\Users\\Owner\\AppData\\Local\\Programs\\MiKTeX\\miktex\\bin\\x64\\lualatex.exe"];
SetOptions[MaTeX,"Preamble"->{"\\usepackage{fontspec}\\setmainfont{Arial}\\usepackage{amsmath}\\catcode`@=11
\\def\\twidehat#1{$\\m@th\\widehat{\\hbox{#1}}$}
\\catcode`@=12"}];
And now
MaTeX["{\\text{\\fontsize{20pt}{16pt}\\selectfont \\twidehat{X}}}"]

Reference:
https://tex.stackexchange.com/questions/647544/widehat-in-text-mode-in-plain-xetex