How can I use Apple Watch to make phone call without cell phone near by?

Your post suggests you already have the watch added to the Verizon plan for your iPhone. That is the starting point, but you don’t say whether it got setup on the hardware. Please see Set up cellular on your Apple Watch - Apple Support as a detailed checklist for what you should have done (or still need to do).

The first critical check is to swipe up for Control Center and check the state of the cellular data button (usually top left). It often seems to default to Off so this is a frequent trap for new users. The button should have either a white background (cellular standby) or green (Cellular is connected). It should not have a black background (cellular off) so tap the button if necessary and enable cellular.

The other thing to be aware about is your watch normally communicates through your iPhone with the cellular radio powered off. Cellular is only activated when the watch loses all other communication routes, and it can take a little time for the cellular radio to connect and negotiate with the network. For a first ever connection it is probably reasonable to allow up to 2 minutes before you panic. Note that it needs all other routes to fail completely before cellular is activated, so you might need to move well away from your iPhone and any WiFi access points it might try to use. In my experience the watch is very good at clinging to the last tiny signal on Bluetooth and WiFi even if the signal is not strong enough to pass useful data.

If you can't connect to Wi-Fi, cellular, or your iPhone. When your Apple Watch is disconnected, you can still do these things. ... You also need to be signed in to iMessage on your iPhone. If you're on Wi-Fi and want to call a phone number, makesure that Wi-Fi calling is turned on for your Apple Watch