The default sorting is the order in which the class or subclass was released.
It does not include classes and subclasses appearing in Unearthed Arcana or third-party works. The following list of Dungeons & Dragons 5th edition character classes includes every character class and subclass which appeared in an official Dungeons & Dragons 5th edition product. A Paladin could cast Firebolt, or Booming Blade a Barbarian could use Vicious Mockery and a Ranger could summon Eldritch Blast. And even these early-level picks are brilliant.