suffix
first doing of ... (ever, in one's life, in the new year, etc.)
Attaches to the -masu stem of a verb to express the first time doing that action, often in a special context like the new year or a lifetime first.
初詣は、新年になって初めて神社にお参りすることです。
Hatsumōde is visiting a shrine for the first time in the new year.
書き初めは、新年に初めて書や絵をかく行事です。
Kakizome is the event of doing calligraphy or painting for the first time in the new year.