I am unable to make a personal voicemail message on my iPhone 8

I am unable to make a personal voicemail message on my iPhone 8 - I have tapped the phone app - then tapped the voicemail icon on the right hand bottom of the screen then there is no icon appearing at the top right hand corner of the screen which indicates I'm able to make a message. The default message states "i am unavailable and the caller is not able to leave a message and the caller is instructed to call back" I did not set up this message.

The advice from Apple support is that it is a carrier problem?

Does anyone please have a suggestion?

Thank you

[Re-Titled by Moderator]