Multiple animated boxes with tikz in beamer

You can use the background library so that the box that includes the others appears in the background.

Here, I did not use this library (I put the code between comments), I used the native possibility of TikZ.

pgfdeclarelayer{background layer}
pgfsetlayers{background layer,main}

documentclass{beamer}
mode<presentation>{usetheme{Madrid}}

usepackage{tikz}
usetikzlibrary{arrows.meta,backgrounds,fit,matrix}
%usetikzlibrary{backgrounds}

tikzstyle{bigbox} = [minimum size=3cm,draw=blue!50, thick, fill=blue!10, rounded corners, rectangle]
tikzstyle{box} = [minimum size=1.5cm, rounded corners,rectangle, fill=blue!50]
tikzstyle{arrow} = [thick,->,>=stealth]

begin{document}
pgfdeclarelayer{background layer}
pgfsetlayers{background layer,main}

begin{frame}[t]
    

begin{tikzpicture}[
every edge/.style = {draw, thick, -Stealth}
                        ]
path (-1,-1)rectangle(1,1);
node (box11) [box] {11};

node<+(1)-> (box12) [box, right of=box11,xshift=2cm] {12};

node<+(1)-> (box13) [box, right of=box12,xshift=2cm] {13};

node<+(1)-> (box21) [box, below of=box11,yshift=-2cm] {21};

node<+(1)-> (box22) [box, right of=box21,xshift=2cm] {22};

node<+(1)-> (box23) [box, right of=box22,xshift=2cm] {23};

%node (box) [bigbox] {P};

path[transform canvas={yshift=+2mm}]<+(1)->
    (box11) edge (box12)
    (box12) edge (box13)
    (box21) edge (box22)
    (box22) edge (box23);
    
path[transform canvas={yshift=-2mm}]<+(1)->
    (box12) edge (box11)
    (box13) edge (box12)
    (box22) edge (box21)
    (box23) edge (box22);

path[transform canvas={xshift=+2mm}]<+(1)->
    (box12) edge (box22)
    (box13) edge (box23);
    
path[transform canvas={xshift=-2mm}]<+(1)->
    (box22) edge (box12)
    (box23) edge (box13);
    
%begin{scope}[on background layer={color=yellow}]
%node<+->[draw,fill=green!50,fill opacity=.5,fit= (box11) (box22)]{box};
%end{scope}

begin{pgfonlayer}{background layer}
node<+->[draw,fill=green!50,fit= (box11) (box22)]{box};
end{pgfonlayer}
end{tikzpicture}
end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%begin{frame}[fragile]
%    
%
%begin{tikzpicture}
%tikzstyle{bigbox} = [minimum size=3cm,draw=blue!50, thick, fill=blue!10, rounded corners, rectangle]
%tikzstyle{box} = [minimum size=1.5cm, rounded corners,rectangle, fill=blue!50]
%
%
%matrix[row sep=20mm, column sep=15mm, inner sep=7mm, bigbox, matrix of nodes, every node/.style=box] {
%11 & 12
%21 & 22
%};
%
%node (h1) [yshift=0mm] {Text};
%
%matrix[xshift=6cm,row sep=20mm, column sep=15mm, inner sep=7mm, matrix of nodes, every node/.style=box] {
%13
%23
%};
%
%
%end{tikzpicture}
%end{frame}


end{document}