Hey Having_Problems1234,
If an Ethernet cable is connected, the Wi-Fi option will not appear, but you do mention this happens when the cable isn't connected too. If you haven't already, reconnect the Ethernet cable to see if you're able to finish the setup for your Apple TV. This will also provide an opportunity for it to check for available software updates, and install them. Updating could help to resolve this issue as updates install bug fixes and security updates.
It's also a good idea to check the Ethernet port for dirt or debris as that can cause odd connections issues too. If any is found, gently clean it out. This guide has information on cleaning and care: Important handling information for Apple TV - Apple Support
The following guide has some great tips and steps on issues related to connecting to a network, including updating using an Ethernet cable which is shown in Step 3: If your Apple TV can't connect to Wi-Fi - Apple Support
Something else important to note from the guide is:
If you want to switch from an Ethernet connection to Wi-Fi
Unplug the Ethernet cable from your Apple TV. You might have to wait several minutes for the Apple TV to notify you that you can join a Wi-Fi network.
Apple TV might be able to join some education or business networks that use a profile. Ask the network's system administrator for more information.
Let us know how it goes.
Take care!