Q: How can I restore my Apple TV without a USB-C cable?

If your device were functioning properly you would be able to restore it using one of the options in the settings menu (Restore your Apple TV to its factory settings - Apple Support) but it it is displaying that screen, and won't let you navigate the menus at all, then you'll need to restore using iTunes. A USB A-C cable isn't that expensive. Alternatively you could make an appointment at an Apple Store Genius Bar or with an Apple Authorized Support Provider and have them reset it for you. See Restore your Apple TV through iTunes - Apple Support.

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