The airfield I soloed at had a 36 ft wide, 01-19 runway, and predominantly westerly winds, which meant that the instructors generally waited for a calm evening and maybe soloed more than one person in a session. This resulted in everybody usually being more than ready to solo when the time came.
So nobody knew a date in advance, but everybody knew that a calm evening made it a possibility.
In my case the student before me got off the ground and turned downwind but then overflew the airport and disappeared into the gathering twilight. I can still see the instructor running into the office to shepherd the student back home again by radio. Had a good effect on me, waiting for my turn to solo, thinking, well I can probably do better than that. However, so much time had passed that I only did one circuit and landed with the disc of the sun sitting on the horizon. A great experience, but I was glad that I didn’t have to land looking into the sun.
Cheers,