The approach you suggest is very ++nice. It can easily be adapted to other cases; e.g., a case in which the comparison may vary with each tuple of indices.

use strict;
use warnings;
use List::Util qw(all);

# create and populate my @matrix as before
...

my @tuples = (
    [1, 0, 4, 0], [2, 0, 4, 1], [3, 0, 4, 2],
    [4, 1, 4, 0], [5, 1, 4, 1], [6, 1, 4, 2],
    ...
    [9, 4, 6, 0], [8, 4, 6, 1], [7, 4, 6, 2],
    );

do_something() if all { $_->[0] == $matrix[$_->[1]][$_->[2]][$_->[3]] 
+} @tuples;
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At a slight performance cost, the subroutine block of  all could be made a bit more readable:
    { my ($n, $i, $j, $k) = @$_;  $n == $matrix[$i][$j][$k]] }