If you don't need BEGIN time, you could try to stuff your routine that works with the data into a CHECK or INIT block.

But it's hard to give an advise without knowing why you need which data at compile time.

Some further context seems indeed to be appropriate.
In our version control system, we have rules to associate the names of some objects with a specific location in a directory structure.
We made a perl wrapping around our VC system to automate this logic and to avoid the creation of too many categories. At that time, we were already faced with a history of objects which did not fit the pattern.
For these objects , hashes were created, as a kind of exception to the rule and these were initialized at the loading the module.
Alas, as so often happens, exceptions proliferated, so this list became rather long, which lead to my question above.
To be short, a (huge) hash has to be initialised at run time.
Tabari

Why can you not just:

my %hugeHash = eval do {local $/; <DATA>};

...

__DATA__
exception1 => 'wibble',
...
[download]

to load your hash from the data section? You could make it a whole lot more robust, but if you want quick and dirty that gets you going.

---

Perl is environmentally friendly - it saves trees

For these objects , hashes were created, as a kind of exception to the rule and these were initialized at the loading the module.

...

To be short, a (huge) hash has to be initialised at run time.

This is still confusing. Are you sure you need to do this in a BEGIN block? If you really need to initialize this hash "at runtime" as you say, then you can do it in normal code. (And if you can do it in normal code, I would suggest calling a sub that returns the hash, rather than using __DATA__.)

Also unclear is whether this initialization is happening in a script or in a module. If it's a module and you just need the hash to be created when the module is used, then again a BEGIN block is not necessary. If, on the other hand, it's in a script and you need the hash to be created before any modules are loaded, then BEGIN is necessary.

It would help to see some actual code here.

If you absolutely need __DATA__ in a BEGIN block, you have to roll your own __DATA__ handling (opening and positioning, i.e. skipping all until the __DATA__ token):

package Foo::Bar::Quux;

print "now in runtime...\n";

BEGIN { 
    (my $package = __PACKAGE__) =~ s!::!/!g;
    my $file     = $INC{$package.'.pm'};
    open DATA , '<', $file
        or die "Can't open '$file': $!\n";

    my $data = 0;
    while (<DATA>) { 
        /^__DATA__$/ and $data = 1 and next;
        next unless $data;
        print "DATA: $_";
    };
}
1;
__DATA__
foo
bar
quux
now in runtime...
now in main
[download]

qwurx [shmem] ~ > perl -e 'print "now in main\n"; use Foo::Bar::Quux'
DATA: foo
DATA: bar
DATA: quux
now in runtime...
[download]

That's for a module. In a script, you would open $0.

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}

Using a heredoc would have the same effect with less magic, although the code layout would be different.

print "now in runtime...\n";

BEGIN {
    open my $fh , '<', \<<'__EOI__' or die;
foo
bar
quux
now in runtime...
now in main
__EOI__

    while (<$fh>) { 
        print "DATA: $_";
    }
}

...
[download]