Try this. Of course, the parameters can be adjusted to change vertical separation height or horizontal width of wedge relative to = sign, or aspect ratio of wedge. Note that the appearance of this is not quite the same as \hateq
cited in comments above, but better conforms to the symbol illustrated by the questioner.
REVISED SOLUTION eliminated use of array
to make space around \equalhat
compatible with \mathrel
.
\documentclass{article}
\usepackage{scalerel,stackengine,amsmath}
\newcommand\equalhat{\mathrel{\stackon[1.5pt]{=}{\stretchto{%
\scalerel*[\widthof{=}]{\wedge}{\rule{1ex}{3ex}}}{0.5ex}}}}
\begin{document}
\[
x^2 \equalhat \ensurestackMath{\Centerstack[c]{a b c}}
\]
\begin{align}
a &\equalhat b \\
a &= b
\end{align}
\end{document}

ORIGINAL SOLUTION
\documentclass{article}
\usepackage{scalerel,amssymb}
\newcommand\equalhat{%
\let\savearraystretch\arraystretch
\renewcommand\arraystretch{0.3}
\begin{array}{c}
\stretchto{
\scalerel*[\widthof{=}]{\wedge}
{\rule{1ex}{3ex}}%
}{0.5ex}\\
=%
\end{array}
\let\arraystretch\savearraystretch
}
\begin{document}
$x^2 \equalhat \begin{array}{c}a\\b\\c\end{array}$
\end{document}

$\cong$
might be what you want. Other related symbols are\simeq
,\sim
,\approx
. There is a symbol bible out on the web called symbols-A4.pdf. Very useful.\func
.\mathrel{\widehat{=}}
might help you. It would help us, if you discribe, what is not good with the commands you found.\mathrel{\widehat{=}}
and\widehat{=}
are actually the same as they will produce the same symbol. The only difference (at least to my knowledge) is, that the former tells tex it is a relation symbol which results in more free space in front and behind it. What ever symbol you use at the end: it might be a good idea to put it into\mathrel{}
for that particular reason.