Otherwise, it will not appear on the list of available networks on your Fire TV stick. You also want to make sure that the Wi-Fi network you're trying to connect your Fire TV stick to isn't hidden. If it is, you should unblock or whitelist your Fire TV stick and try reconnecting to the Wi-Fi network. You should also check the router's admin panel to confirm that your Fire TV stick isn't blocked or blacklisted. You could also manually assign your Fire TV stick its unique IP address via your router's DHCP menu. If the number of connected devices on the router has hit the set limit, you can either increase the number of simultaneous connections (if possible) or disconnect one device to make room for the Fire TV stick. You should check that the router doesn't have a DHCP disabled else you have to assign a static IP to the Fire TV stick. To start off, one of the ideal troubleshooting moves is to confirm that the Wi-Fi router is indeed functioning properly and doesn't have any limitation that's preventing the Fire TV stick from connecting to the router.

If you are facing issues with connecting Fire TV stick to a Wi-Fi network, then you need to check a few things with your router first. Check for Router Limitations/Restrictions