.the first time 用来引导状语从句
分析：
on the first time是介词短语,只能作状语,不能接从句；the first time相当于一个连词,引导状语从句,同时定冠词the不能省略,故选B.
〔透视〕the first time/day,the moment/minute/second,immediately,every time,next time等表示时间的名词短语可用作连词,引导时间状语从句.time构成的搭配还有：at a time 一次；at one time 曾经；all the time 一直、总是；at times 时常；from time to time 间或；in time 及时；on time 准时；time and time again 一次又一次；at the same time 与此同时.