Hi Jsackie95,
Thanks for coming to Apple Support Communities for help restoring your MacBook Air to factory settings. It sounds like you went into Recovery and couldn't connect to Wi-Fi.
Go ahead and try once more with your Wi-Fi connection if you have previously been connecting to Wi-Fi without issue. Have a look at this page and double-check the steps: How to reinstall macOS from macOS Recovery. Follow "If you never installed macOS Sierra 10.12.4" if this is the case. If you have, then you will hold down Shift-Option-⌘-R at boot up.
Using a mobile hotspot may not be the best solution because of the amount of data that will be downloaded. You should try another Wi-Fi network if possible. If that still won't work, you would need a wired connection. Depending on your MacBook Air model, you would need to buy an Ethernet adapter with either a USB connection or Thunderbolt connection. Check out: Thunderbolt to Gigabit Ethernet Adapter and Apple USB Ethernet Adapter.
Have a fantastic day!