Hi -
I seem to remember the same thing. It was hard to find any verification of the sign-up. Maybe choose something that is not available on Prime Music (if you are a Prime member) and see if it will play on the device. I just looked through the history on my Alexa app and found where it said "Welcome to Amazon Music Unlimited" after I signed up.
Maybe you've already resolved this- if not, hope this helps. If all else fails, you could call them. 😃