with time passing by,out school will more and more beautiful.

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.