for the first time是一个介词短语,在句子中作状语; the first time做连词,可以引导一个时间状语从句. 例如: I met her for the first time. 我第一次遇到她. The first time I met her, I thought she was an honest person. 或者:I thought she was an honest persone the first time I met her. 第一次遇到她的时候,我认为她是一个诚实的人.