NOTE: the free trial will only work for testing the CAS API. This detail is not currently posted on their website or mentioned in their guides. You cannot use it for live SMS messaging (only for testing).
The The “free trial” number they provide may not work (for testing) for the first few days. Try sending a test from the Nexmo dashboard - if it works, then the CAS API test should also work.
You will have to add funds to:
procure a toll-free number, or
register a brand and campaign to send messages in the USA.
Either method will work, but each has it’s hurdles:
See: 10DLC (below)
An alternative for testing messages in the USA (that does not require immediate 10DLC registration) is purchasing and using a toll-free number (i.e., https://dashboard.nexmo.com/buy-numbers). However, the toll-free number will also get blocked after sending multiple messages in a short period of time. Eventually, a toll-free number also needs to be verified to prevent blockage.