You wake around 3 a.m. because the second half of the night is lighter. Sleep runs in cycles of about 80 to 100 minutes, and the later cycles carry more REM, which is easier to leave. It is not a 3 a.m. cortisol spike. Cortisol stays low through the early night and peaks near your usual morning wake.
The second half is lighter
The first half of the night holds more deep sleep. Later cycles are dream-heavy, and dream sleep sits closer to waking. A noise, a warm room, or a full bladder is more likely to register then. Waking is not, by itself, a sign that the night failed. A bright phone or a clock check is what usually keeps that short wake going. The hour itself is not the cause.
Cortisol is not the 3 a.m. alarm
Cortisol, a hormone that helps you get up, stays low through the early night. It rises toward your usual morning wake, and it peaks around that wake, not at 3 a.m. If you are awake at 3, you are in the lighter part of the night, when waking is simply easier.
If this happens often and the day feels it, a clinician is the person who sorts that out. This note does not promise the waking will stop.
The room can make that lighter sleep easier to leave. Why a cool, dark room helps.