Take 日, the sun you already know, and set it above a single flat stroke. The oldest dictionaries read that stroke as the horizon: the instant the sun's disc touches it, night breaks into day — dawn drawn as literally as a sunrise can be drawn.
A piece of culture
New Year's dawn 元旦 (yuándàn), literally "first dawn", is the Chinese name for New Year's Day on the solar calendar — a separate holiday from the much bigger Lunar New Year weeks later. 旦 also names a whole category of female roles in Chinese opera, 旦角 (dànjué), and for a long stretch of Peking opera's history male actors specialized in playing them, most famously Mei Lanfang in the twentieth century.