No, you can not. Only holders of an EU passport, or a passport from one of the four EU associate countries (Liechtenstein, Switzerland, Norway or Iceland) can become a Privium member. UK passport holders are an exception - they can no longer apply for a new membership, but current memberships are honored and can be renewed, with a slight change in service - they will never pass directly through at immigrations, but the system will always direct them through the "failure" lane to a manned booth.
US passport holders can not currently apply for Privium, and there is no timeline for that either. They are working on RTP-NL, which would give non-EU passport holders access to the automated passport control lanes, after registration. However, the RTP-NL launch has been pushed back for years now. The latest communicated launch date was april 2022, but that has again passed.