I would not think that a 32MB file should be a problem unless you have a tiny computer. But you could count the aminoacids while reading the file:

#!/usr/bin/perl
use strict;
use warnings;
use diagnostics;

my %count;
open PROTEOME, '<', 'human_complete_proteome_without_isoforms.fasta';
while(<PROTEOME>){
    next if /^>/;
    chomp;
    $count{$_}++ for split //;
}

print "hash has finished searching the document\n";
foreach (keys %count)
{
    print "$_ \t occurs $count{$_} times \n";
}
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