s/^.//;
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What if the first character is a newline? :-) Don't forget the /s! As an aside, FWIW, the s/// is much less efficient than the substr solution here.

Another overengineered way:

use Fcntl qw( :seek );

$_ = "12345";

{
    open my $fh, "<", \$_;
    seek $fh, 1, SEEK_SET;
    local $/;
    $_ = <$fh>;
}
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