noun
first birdsong of the New Year
Specifically refers to the first warbling or chirping of birds heard at the beginning of the New Year, often associated with the uguisu (Japanese bush warbler). A poetic and seasonal term.
元旦の朝、庭から初音が聞こえてきた。
On New Year's morning, I heard the first birdsong of the year from the garden.
初鳴き also means 'first chirp/cry' but is used more broadly for the first vocalization of any animal or insect in a season, not specifically the New Year.
Compound of 初 (hatsu, 'first') and 音 (ne, 'sound'). The reading ね for 音 is an older native Japanese reading. The term is traditionally associated with the first song of the uguisu in the New Year.