also: はつそら
noun
New Year's morning sky
Refers specifically to the sky seen on the morning of New Year's Day, often with a poetic or auspicious feeling.
初空を見ながら今年の目標を考えた。
I thought about my goals for the year while looking at the New Year's morning sky.
初日の出 refers to the first sunrise of the year, while 初空 is the sky itself on New Year's morning, not limited to sunrise.
Compound of 初 (hatsu, 'first') and 空 (sora, 'sky'), referring to the first sky of the new year.