Do you need the conventional remote to set it up, even if you can later use your phone to control it?
Correct, at least until both devices are connected to the same home network. Before that, entering the network settings would require a physical remote (that doesn’t rely on a network connection).
If you lost the remote for your Apple TV - Apple Support
Apple TV HD, tvOS 12
That unit hasn’t seen updates in a very long time. We’re on tvOS 15.5.1 now. It is strongly recommended to keep your devices up-to-date (at your earliest convenience). Update your Apple TV - Apple Support.
The current official replacement remote requires tvOS 14.5 or later. So, that seems like a “catch 22”. You could use the old style remotes, borrowed or bought second hand, to work around that. Else contact Apple for updates that you can’t do yourself.