A matrix with first row and column spanning over a sub-matrix

By adapting the code of the OP:

documentclass{article}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
   
begin{document}
begin{center}
    [
    P= 
    left[
    begin{matrix}
    1      & 1 & dots                & 1 & 1                     & 1 & dots             & 1  \
    1      &   &                      &   & multicolumn{1}{c|}{}  &                       &    \
    vdots &   & textbf{Huge{C}}    &   & multicolumn{1}{c|}{}  &   & textbf{Huge{0}} &    \
    1      &   &                      &   & multicolumn{1}{c|}{}  &   &                        \
    cline{2-8}
    1      &   &                      &   & multicolumn{1}{c|}{}  &   &                        \
    vdots &   & textbf{Huge{0}}    &   & multicolumn{1}{c|}{}  &   &textbf{Huge{D}}       \
    1      &   &                      &   & multicolumn{1}{c|}{}  &   &
    end{matrix} ;
    right]
    ]
end{center}
end{document}

Like this? I use nicematrix package to redraw the matrix, the key point is first-row option.

documentclass{article}
usepackage{nicematrix}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}

begin{document}
[
p=left[
begin{NiceArray}{*4{C}|*3{C}}[first-row, extra-margin=2mm]
  1 & 1 & Cdots & 1 & 1 & Cdots & 1 \
  1 & Block{3-3}<Huge>{mathbf{C}} & & & Block{3-3}<Huge>{mathbf{0}} & & \
  Vdots & & & & & & \
  1 & & & & & & \
cline{2-7}
  1 & Block{3-3}<Huge>{mathbf{0}} & & & Block{3-3}<Huge>{mathbf{D}} & & \
  Vdots & & & & & & \
  1 & & & & & & \
end{NiceArray}right]
]
end{document}

With array and some nesting:

documentclass{article}
usepackage{amsmath,array}

newcommand{bigentry}[2][huge]{begin{tabular}{@{}c@{}}#1$#2$end{tabular}}

begin{document}

[
newcommand{ones}{begin{matrix} 1 \[-1ex] vdots \ 1 end{matrix}}
left[begin{array}{ c @{} c | c @{} }
noalign{vspace{0.5ex}}
begin{matrix} 1 end{matrix} &
multicolumn{1}{c@{}}{begin{matrix} 1 & dots & 1 end{matrix}} &
begin{matrix} 1 & dots & 1 end{matrix} \
ones & bigentry{mathbf{C}} & bigentry{mathbf{0}} \
cline{2-3}
ones & bigentry{mathbf{0}} & bigentry{mathbf{D}} \
noalign{vspace{0.5ex}}
end{array}right]
]

end{document}

We need a couple of tricks because of vdots not being really suitable for the purpose, so some vertical space has to be added at the top and the bottom.

Avoid textbf for math objects in formulas, it should be mathbf.

The nested tabular for bigentry ensures vertical centering and can accommodate a size changing command, which would otherwise be illegal in math mode.

The command ones is just a local shorthand for reducing code clutter.

A proposition with nicematrix:

documentclass{article}
usepackage{nicematrix}
usepackage{tikz}
   
begin{document}

$begin{pNiceArray}{ccccr}[columns-width=4mm,right-margin,nullify-dots]
1       & Cdots & &                        & 1 \
Vdots  & Block{2-2}<Large>{C} & & Block{2-2}<Large>{0} &   \
\
  & Block{2-2}<Large>{0} & & Block{2-2}<Large>{D} &   \
1 
CodeAfter
tikz draw (4-|2) -- (4-|6) (2-|4) -- (6-|4) ;   
end{pNiceArray}$

end{document}