Tcolorbox : create a proof environnement with a QED symbol at the very end

Add the lines

\usepackage{amssymb}% defines \blacksquare
\AtEndEnvironment{proof}{\null\hfill\textcolor{blue}{$\blacksquare$}}

to your preamble; replace \blacksquare by \square if the symbol is too massive.

For LaTeX versions older than 2020/10/01, you need the etoolbox package before using \AtEndEnvironment.

\documentclass{article}
\usepackage{amssymb}
\AtEndEnvironment{proof}{\null\hfill\textcolor{blue}{$\blacksquare$}}%
\usepackage{changepage}
\usepackage{tcolorbox}
  \tcbuselibrary{most}

\newtcolorbox{proof}{
  fonttitle=\bfseries,
  enhanced,
  top=0mm,
  boxrule=0pt,frame empty,
  borderline west={4pt}{0pt}{blue},
  coltitle=blue,
  colback=white,
  sharp corners,
  title=Proof
}

\begin{document}
\begin{proof}
  Let's show that girls are Evil.
  \begin{adjustwidth}{5mm}{0mm}
    So, girls are evil:
    \begin{equation}
      girls = \left(\sqrt{evil}\right)^2 = evil
    \end{equation}
  \end{adjustwidth}
  We have shown that girls are Evil.
\end{proof}
\end{document}

Adapted from this answer

Using the ntheorem package, you have the automatic placement of the end-of-proof symbol at the end of the last line, including the cases when the last line is an equation:

\documentclass{article}
\usepackage{fourier} 
 \usepackage{amsmath, amssymb}
\usepackage[thmmarks, amsmath, thref]{ntheorem}
\usepackage{changepage} 
\usepackage{tcolorbox}
\tcbuselibrary{most}

\theoremstyle{nonumberbreakn}
\theoremheaderfont{\scshape\color{blue}}
\theoremseparator{:\smallskip}
\theorembodyfont{\upshape}
\theoremsymbol{\ensuremath{\color{blue}\blacksquare}}
\newtheorem{proof}{Proof}

\tcolorboxenvironment{proof}{
  fonttitle=\bfseries,
  enhanced,
  top=0mm,
  boxrule=0pt,frame empty,
  borderline west={4pt}{0pt}{blue},
  coltitle=blue,
  colback=white,
  sharp corners
}

\begin{document}

\begin{proof}
  Let's show that girls are Evil.
  \begin{adjustwidth}{5mm}{0mm}
    Girls require time and money
    \begin{equation}
      girls = time \times money
    \end{equation}
    Time is money
    \begin{equation}
      time = money
    \end{equation}
    So girls are money squared:
    \begin{equation}
      girls = money^2
    \end{equation}
    Money is the root of all evil
    \begin{equation}
      money = \sqrt{evil}
    \end{equation}
    So, girls are evil:
    \begin{equation*}
      girls = \left(\sqrt{evil}\right)^2 = evil
    \end{equation*}
  \end{adjustwidth}
% We have shown that girls are Evil.
\end{proof}

\end{document}