Fetching details from the dictionary...

first doing of ... (ever, in one's life, in the new year, etc.)
今年の泳ぎ初めは海だった。
My first swim of the year was at the sea.
書き初めを半紙に書いた。
I wrote the first calligraphy of the year on calligraphy paper.
着初めのワンピースで出かけるのが楽しみだ。
I'm looking forward to going out in my new dress for the first time.