Why is there no Wi-Fi option on the 'Activate Mac' screen?

What year model is your Mac mini and what macOS version was it running..?

Identify your Mac mini model - Apple Support

What method did you use to erase the Mac mini's internal hard drive...?

Use Disk Utility to erase an Intel-based Mac - Apple Support

Try Option-Command-R to start up from Internet Recovery.

How to reinstall macOS - Apple Support

"activate mac screen showing no wifi option: i erased my hard drive on my mac mini and restarted and got an activate mac screen. i have an active wifi but no options to access it."

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Activating WiFi:

To activate WiFi, click on the WiFi emblem located on the top-right corner of the screen. If you do not see your network, then you may not be broadcasting the SSID (the name of the network), in which case, you ender it manually, along with the password.