I'm guessing this will also delay systemctl start myunit.service. Is there a way to delay the timer only, and not the service itself, so that manual runs skip the delay?

I don't see any systemd way to do that. I added a variant that only runs the sleep command if the uptime is sufficiently low. It's more a dirty hack, but this kind of delay is sort of a hack anyway.

For systemd timers specifically OnBootSec= looks promising.

Thank you! For others - with systemd, the action has to be one command anyway, so if it's complex you have to wrap it in a script. So the way to skip the delay in manual runs would appear to be to run the script directly rather than the unit.

You would still have the problem of annoying delays while testing it. But I guess you can temporarily comment out the delay until you're done testing.

And, looks like if I set both OnBootSec and OnCalendar it will somewhat solve my problem. The OnCalendar will fire right after boot and fail, but a few minutes later OnBootSec will trigger again and this time succeed. My use case would be okay with an occasional fail, so long as there's a success soon after.

You could replace with OnCalendar with OnUnitActiveSec (and make sure not to make it Persistent). And then remove any delays from the service itself.