Matrices upper triangular alignment

Here are two versions as I am not sure if you want the central element on or off the diagonal

where

• I have used\mathrlap to hide the subscript and superscript from affecting column width so that the \ddots appear below them,
• used \smash on the large zero so it does not effect vertical spacing,
• used \multicolumn{}{}{} for the case on central element being off the diagonal, and
• eliminated unneeded packages for this example.

Code:

\documentclass{article}
\usepackage{mathtools}

\newcommand*{\A}{((\hat{\Phi}(p)_{ij}))\mathrlap{{}_{i,j=1}^r}}%
\newcommand*{\B}{((\partial^{\alpha}\partial^{\beta}\hat{\Phi}(p)_{ij}))\mathrlap{{}_{i,j=1}^r}}%
\newcommand*{\C}{((\partial_d^{k-1}\hat{\Phi}(p)_{ij}))_{i,j=1}^r}
\newcommand*{\BigZ}{\hspace*{2.0em}\smash{\text{\Huge0}}}

\begin{document}
\[ 
   J(\hat{\Phi})(p)=
   \begin{pmatrix*}[c]
     \A  &        & \hdots  &  \hdots & \A     \\
         & \ddots &         &         & \vdots \\
         &        & \B      &         & \vdots \\
   \BigZ &        &         & \ddots  & \vdots \\
         &        &         &         & \C     \\
\end{pmatrix*}
\]
\end{document}

Code: Central Element off Diagonal

\documentclass{article}
\usepackage{mathtools}

\newcommand*{\A}{((\hat{\Phi}(p)_{ij})){{}_{i,j=1}^r}}%
\newcommand*{\B}{((\partial^{\alpha}\partial^{\beta}\hat{\Phi}\mathrlap{(p)_{ij})){}_{i,j=1}^r}}%
\newcommand*{\C}{((\partial_d^{k-1}\hat{\Phi}(p)_{ij}))_{i,j=1}^r}
\newcommand*{\BigZ}{\hspace*{2.0em}\smash{\text{\Huge0}}}

\begin{document}
\[ 
   J(\hat{\Phi})(p)=
   \begin{pmatrix*}[c]
     \A  & \hdots & \hdots  &  \hdots   &  \hdots    & \A     \\
         & \ddots &         &           &            & \vdots \\
         &        & \ddots  & \multicolumn{2}{c}{\B} & \vdots \\
   \BigZ &        &         & \ddots    &            & \vdots \\
         &        &         &           & \ddots     & \vdots \\
         &        &         &           &            & \C     \\
\end{pmatrix*}
\]
\end{document}

If you are open to loading tikz, you could do

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{tikz}
\usetikzlibrary{tikzmark}
\begin{document}
\[ J(\widehat{\Phi})(p)=
   \begin{pmatrix*}[c]
   \tikzmarknode{tl}{((\widehat{\Phi}(p)_{ij}))_{i,j=1}^r}   & 
   \hspace*{9em}&
    \tikzmarknode{tr}{((\widehat{\Phi}(p)_{ij}))_{i,j=1}^r}    \\[4em]
 \tikzmarknode{bl}{~} &  &
 \tikzmarknode{br}{((\partial_d^{k-1}\widehat{\Phi}(p)_{ij}))_{i,j=1}^r}
\end{pmatrix*}
\begin{tikzpicture}[overlay,remember picture,Dotted/.style={%https://tex.stackexchange.com/a/101263/194703
 line width=#1, line cap=round, dash pattern=on 0pt off 4\pgflinewidth},
 Dotted/.default=1.5pt,shorten/.style={shorten >=#1/2,shorten <=#1/2}]
 \draw[Dotted,shorten=4ex]  (tl) -- (tr);
 \draw[Dotted,shorten=4ex]  (tr) -- (br);
 \draw[Dotted,shorten=5ex]  (tl) -- (br) node[pos=0.5,inner sep=0pt,above
 right]
  {$((\partial^{\alpha}\partial^{\beta}\widehat{\Phi}(p)_{ij}))_{i,j=1}^r$} ;
 \node[scale=3,above] at (bl.south west) {$0$};
\end{tikzpicture}
\]
\end{document}

You could also work with nicematrix (which uses TikZ).

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{nicematrix}
\begin{document}
\[ J(\widehat{\Phi})(p)=
   \begin{pNiceMatrix}[name=mymatrix]
   ((\widehat{\Phi}(p)_{ij}))_{i,j=1}^r   & 
   \Cdots \Hspace*{7em}& ((\widehat{\Phi}(p)_{ij}))_{i,j=1}^r\\[2em]
   &\Ddots & \Vdots \\[2em]
 ~ &  & 
  ((\partial_d^{k-1}\widehat{\Phi}(p)_{ij}))_{i,j=1}^r\\
\end{pNiceMatrix}
\begin{tikzpicture}[overlay,remember picture]
 \path (mymatrix-1-1) -- (mymatrix-3-3)
 node[pos=0.5,above right,inner sep=0pt]
   {$((\partial^{\alpha}\partial^{\beta}\widehat{\Phi}(p)_{ij}))_{i,j=1}^r$} ;
  \node[scale=3,above] at (mymatrix-3-1) {$0$};
\end{tikzpicture}
\]
\end{document}

Something like this?

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools,amssymb}
\begin{document}
\[
\setlength\arraycolsep{2.5pt} % default value: 5pt
J(\widehat{\Phi})(p)=
\begin{pmatrix}
\bigl((\widehat{\Phi}(p)^{}_{ij})\bigr)_{i,j=1}^r &\dots &\dots & \dots & 
       \bigl((\widehat{\Phi}(p)^{}_{ij})\bigr)_{i,j=1}^r \\
& \ddots & \vdots & & \vdots\\
& &\bigl((\partial^{\alpha}\partial^{\beta}\widehat{\Phi}(p)^{}_{ij})\bigr)_{i,j=1}^r & & \vdots \\
 & & & \ddots  & \vdots \\
 \hbox{\huge0} & & & & \bigl((\partial_d^{k-1}\widehat{\Phi}(p)^{}_{ij})\bigr)_{i,j=1}^r
\end{pmatrix}
\]
\end{document}