When I'm going to sleep at reasonable time I wake up within 5 minutes of 06:00 no matter if I set the alarm or not. When I'm not having enough sleep I wake up

When I'm going to sleep at reasonable time I wake up within 5 minutes of 06:00 no matter if I set the alarm or not. When I'm not having enough sleep I wake up after alarm goes off, and usually it's already beeping for a few good minutes, before it wakes me. And I do notice immediately that it's after the alarm. So I doubt waking before alarm is an ilussion.