Empirically there is essentially no minimum distance/time, as the AirTag sound can be triggered by not being near a known device &and moving &and being near an unknown device as soon as this criteria is met.
Unfortunately I don't have citations for this, but I have regularly triggered this behaviour inadvertently, especially when the unknown device is an iPhone that pops the ‘AirTag moving with you’ notification, on a journey of only a few minutes/miles.
