Fetching details from the dictionary...
early morning; early hours; early in the morning
試験勉強で朝方まで起きていた。
I stayed up until the early morning studying for the exam.
明日の朝方は冷え込みが厳しくなるでしょう。
It will probably get quite cold in the early morning tomorrow.
鳥の声で朝方に目が覚めた。
I woke up in the early morning because of the birdsong.