This is a step-by-step, start-to-finish guide to configure a Raspberry Pi as a network storage device for macOS Time Machine backups.

A few things to get out of the way before proceeding:

(*) Since we are talking about Time Machine, I assume you have at least one Mac in your possession with working SSH client.
(*) You are not afraid of Terminal and comfortable with command line.
(*) I also assume that the Time Machine backups will be encrypted, so we won’t be dealing with encryption on the Raspberry Pi end.