I don't know where you are, but our experience might help. DS was not allowed to skip *into* kindergarten, even though everyone knew he should, but the law did allow him to skip *over* kindergarten the next year. So he had two years of preschool, then entered first grade at age 5, turning six a week later. His birthday was a week past the cutoff. You might try asking about that.
In the meantime, if he likes school, that's a big plus. If he has a teacher that will give him more stuff to do, to keep him liking it, that's even better.
