If I were asked to make some kind of notification sound for someone, here are some questions I’d want answered:
medium (physical): What kind of speakers? How loud? What’s the frequency response? What’s the range of playback devices? Maybe there’s more than one place it is expected to go?
medium (software): by this, I mean restrictions related to the playback environment inside the device. Limited duration? File size? Sampling rate? Is it some kind of MIDI/soundfont thing or module format? Something restricted to a fixed-channel chiptune like the gameboy/NES/SID?
Space/environment: What kind of spaces will this be played in? Will it need to compete with other sounds, such as in a busy airport or bar?
Intelligibiliy/information: If applicable, how much information is being conveyed in the notifications (or set of notifications), and how distinguishable do they need to be?
Psychology: how do you want people to react to your sound? Is it mission-critical that they hear the sound at all costs? Or is it a gentle nudge? Are they going to need to be cheered up? chilled out? calmed down? This can get specific, and can also tie into…
…Branding: In a professional setting, usually a company will try to aim for a particular product vibe or distinctness. This ties into pyschology, distinctness, the “stickiness” factor of the particular sound or hook, and general aesthetics. probably not for
Regulations: if applicable, are there legal requirements or standards for the sound? this usually comes into play for things like medical devices, which can be very particular about what goes into an alert or notification sound. The creativity here then would involve working within these constraints to create something interesting that is more than just ticking the boxes.
From there, I can start thinking about what to do.