Etihad has perhaps the most aspirational First Class product in their A380 “First Apartment”. They only fly their A380 to one destination in the U.S. (New York JFK) so space can be hard to find.
According to View from the Wing, Etihad has opened up a bunch of space from Abu Dhabi to New York JFK starting in June. The additional space is most likely coming online because they will begin flying a second A380 on that route as of then.
Searching & Booking
Etihad Guest space can be found directly on their website. Etihad partners with American Airlines, ANA and Korean Air. Any award that shows up in the “Guest Seat” category should be bookable via their partners. You can also transfer Citi ThankYou and American Express Membership Rewards points to directly to Etihad.
For more info and analysis: see, this View from the Wing post.