Only child; both parents oldest siblings. Of course this configuration isn't monstrously rare; we should expect a fair few instances just by chance.

I wonder if being the first-born is genetically heritable.

This is probably just intended as a joke; but it seems pretty plausible that having few children is heritable (though it had better not be too heritable, else small families will simply die out), and the fraction of first-borns is larger in smaller families.