I have just been through this process, so let me clear up a few mistakes or outdated info in this thread:

Privium is open to EU citizens and now also to US citizens who have already been accepted to the GOES program.

There WAS a CBP officer in AMS until 24.2 and he will not be back until end April or May.

Normal process for US Citizens: Sign up for GOES (checking that you want FLUX, i.e. Privium also), perform GOES interview, recieve GOES sticker in passport, perform Privium interview and iris scan.

WHEN a CBP officer is "in residence" in AMS, this may all be completed there, if you ask for the FLUX interview. They will NOT let you have the Privium interview and scan until you have the CBP sticker from GOES in your passport. So for US passport holders, this means that you have to have a trip to the US before completing the process in AMS.

Just a warning. Membership in the GOES program means that if CBP ever catches you out on something, they will throw the book at you. They were very explicit with this. They call it a "trusted program" and if you cheat, they will nail you to the wall.