你这个句子打字有误,应该是：
With time passing by,(our) school will (be)more and more beautiful.
With time passing by,是独立主格结构
独立主格结构要用with连接这个结构的主语.独立主格机构整体充当句子的状语,通常标伴随状况.
例如：
With the war over,people began to produce much food.
With a book under his arm,he arrived here.