for the first time 【首次】单独使用,作时间状语.
I went to Beijing in 2008 for the first time.
at first 【开始、起先】作时间状语.
At first,I didn't recognize her.
the first time 【首次】,不能单独使用,引导从句.
The first time I met her,I thought she was a young woman of intelligence.
it was the first time+从句【是第一次.】
It was the first time that I had been there.