The game board is randomised without any checks on movability, so it can happen that you are stuck in the beginning if you are surrounded by the dark hexagons. Just start a new game in that case.
For advancing, you need to first collect two diamonds or gems for the Malkuth level. Then you start to get moons for the second sephirah, which is Yesod. When you have three gems and two moon, you start to get Hods (Mercurius) on the boards and so on.
I just added more information about the symbology and philosophy on the game page, that acted as inspiration for this game.