Are you running a 32-bit perl?

It works for me for longer strings:

#! /usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

my $long_string = 'ab' x 3e9;
my $pos = index $long_string, 'ba', 6e9 - 4;
say $pos;

__END__
5999999997
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