Tap Voicemail, then tap Set Up Now. Create a voicemail password. Choose a greeting-Default or Custom; if you choose Custom, you can record a new greeting. See More...
Go to your phone Settings and open Cellular option. Now tap on the toggle for Cellular Data option. Turning on the Cellular data; Try using your voicemail and see if the problem still exists. Method 3: Setup Your Visual Voicemail. If you are unable to set up your voicemail through phone settings, then you can try setting it up through your carrier.

Your network can be the culprit causing the issue for the application. Sometimes, the network can be blocking the application usage for your phone. Several users solved this issue by resetting their network settings. Resetting network settings will renew all the information related to the network that you are using on your phone. You can reset the network settings by following the steps below:
Android phones can access voicemail by holding down the 1 key on the dial pad until the phone dials your 10-digit phone number. You will automatically connect to your mailbox and be prompted to enter your temporary password; this password is the last 4 digits of your phone number followed by the # key. Start the Google Voice app. Tap the three horizontal lines at the top left of the screen (sometimes called a hamburger menu), and then tap “Settings.” In the Voicemail section, tap “Voicemail greeting.” Tap “Record a greeting.” How do I access my voicemail? To call your voicemail on an Android phone, simply open your phone’s dial pad and hold your finger down on the “1” key. You can also call your voicemail from a different phone by calling your own number and tapping the pound key. How do you check your voicemail?