not a teacher
If someone told me they had "slept early" I would not be sure what they meant, and would probably ask for clarification.
"Do you mean you went to bed early or woke up early?"
The link charlie has provided seems to use the term for both situations: Should you sleep early…?. "Going to bed early and waking up early is ideal to support your weight loss goals."
In my experience people usually say something like "I went to bed/turned in/retired early", "I was early to bed last night", "I got to sleep early", not "I slept early".
If they mean waking up early: "He woke up/was awake early" "She got up/rose early", "They were up early", and "She's an early riser" or "She wakes up early", not "She's an early sleeper".