The Apple TV models A1625 or later require the Siri Remote (1st, 2nd, or 3rd generation). Additionally, the 2nd and 3rd generation remote have a system software version requirement. Depending on the software version of the Apple TV box, that could potentially put you in a Catch 22, where you need to update to pair the remote, and you need to pair the remote to do an update.
Identify your Apple TV remote - Apple Support
Siri Remote (3rd generation) requires tvOS 15.4 or later (March 2022).
Siri Remote (2nd generation) requires tvOS 14.5 or later (April 2021).
Siri Remote (1st generation) requires tvOS 9.0 or later (Oct 2015), same as the introduction of model A1625.
While an even older Apple TV Remote (e.g. A1294) wouldn’t give full functionality for daily use on a ‘modern’ Apple TV box, but it is compatible and enough to do a software update.
A temporary borrowed compatible remote would be sufficient to do an update.
The software remote on an iPhone would be sufficient to do an update. It can be someone else’s iPhone.
Else make a reservation for updating at the service department of an Apple Retail Store or an Apple Authorized Service Provider.
To pair a Siri Remote with the Apple TV box (A1625 or later), follow this guide: Pair an Apple TV remote with an Apple TV box - Apple Support. Use the button combination as described: “<” Back (or Menu) and Volume Up (“+”) simultaneously.
Else try restarting the remote itself, or charge the remote if needed. If your Siri Remote or Apple TV Remote isn't working - Apple Support