To set up Visual Voicemail, tap Set Up Now. You’ll be prompted to enter and confirm a voicemail password. Next, you’ll have the option to choose the default voicemail greeting or record your own. If you want to record your own custom greeting, tap Custom. Once you’ve entered created your password and chosen your greeting, you’ll be able to receive voicemails and view them in the Phone app.
To change the voicemail greeting on your iPhone, use the steps in this help page - Visual voicemail - iPhone. Specifically -. Update your greeting. Tap Voicemail, tap Greeting, tap Custom, then tap Record. Or, to use your carrier’s generic greeting, tap Default. Thanks for using Apple Support Communities. Be well.

Thanks for the explanation. It does indeed sound like there’s no convenient solution till your whole system gets revamped. To briefly explain *why* I don’t want your voicemail enabled: I use my USMobile number as a forwarding line for Google Voice. Google Voice’s voicemail is frankly superior to yours so I want to use it exclusively. When your voicemail kicks in it interferes with Google Voice’s operation, causing me frustration and a real mess. I’ll give some thought to whether I want to be bothered with going through a quarterly exercise of calling and re-disabling your voicemail.
In the Voicemail section, tap Voicemail greeting. Tap Record a greeting. Tap Record . Record your greeting and when you’re done, tap Stop . Choose what you want to do with the recording: To listen to the recording, tap Play . To replace the recording, tap Redo. To save the recording, tap Save. Enter a name for the new greeting and tap Save.