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first doing of ... (ever, in one's life, in the new year, etc.)
「初め」 has another reading with different meanings.
書き初めを丁寧に書いた。
I carefully wrote my first calligraphy of the year.
今年の走り初めは近所の公園だった。
My first run of the year was at the neighborhood park.
仕事初めの日はみんなで挨拶を交わした。
On the first day back at work, everyone exchanged greetings.