If you want to avoid connecting until you need a connection, you can do this:

my $dbh;

sub dbConnect {
  return if defined $dbh; # exit if we are already connected.
  my $dsn = "DBI:mysql:database:localhost";
  my $db_user_name = 'username';
  my $db_password = 'password';

  $dbh = DBI->connect
    ($dsn, $db_user_name, $db_password, {RaiseError => 1}) || 
         die("cannot connect to DB: ".DBI::errstr."\n",$dbh);
  
}

sub foo {
    # Can still see $dbh in here
    dbConnect();
    my $sth = $dbh->prepare(...);
}
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Since dbConnect() is called each time we want a connection (and not until then), and since it returns if we are already connected, $dbh becomes a persistent connection that is made the first time it is needed.

This method also opens the door for disconnecting from the DB and reconnecting later, if that should ever become useful. (Admittedly, I can't think of when that might be useful, but you never know. ;-P)

Then again, you might just use connect_cached. Though that does something ever-so-slightly different.