A simple workaround has been uncovered in the Too Human demo that allows access to all classes found in the full game, besides the Champion.
If you fancy getting a bigger taste for the game than you first thought, disconnect from the internet and, in the 360 dashboard, change your console date to anytime in or after 2009.
Then, start a new campaign the the demo, and the Berserker and Commando classes should be unlocked in the character selection screen.
In order to get to the Defender and Bioengineer classes, push the left analogue stick to the right as you select either class by pressing A. When you start the game, it will be in whichever of the classes you selected.
To get to the rest of what the game has to offer though, you'll have to wait for the game's release. It hits the shelves on 29th August exclusive to Xbox 360.