Current state

Alpha

The game is currently in Alpha state according to the developer. Sign-up for joining alpha-testing is available through the official Pax Dei website and may involve an NDA.

The first wave of Alpha testers will be invited "before too long™" and will start in a region of Gallia.
Here are the two most current quotes from the developer which gives a more detailed answer to the current state of the game/testing:

We’re still a few months away from a large-scale Alpha test. Rest assured that when we’re ready to announce it, we’ll publish official communication with all details.

We are running regular, small playtests under NDA with our friends and family to test parts of the game we intend to have available for larger-scale testing. One should start pretty soon, actually. We’re sorry we can't add you to these playtests, but they will primarily be used to test specific features and setups in preparation for the Alpha which we can invite you to.