Since the first time we met, President Obama and I have gotten along very well.
This is my first time dealing with banking and I'm really struggling.
"Is it possible this is your first time in Japan?" "Yes, it is." "Oh really? How do you like it?” "I really like it!"
You know that 初 means "first" This word means for the first time. Think of めて as "meet." Then think "when we met for the first time ____ happened."
This word uses the kun'yomi, which you didn't learn with the kanji, so here's a mnemonic to help you out. What are you beginning? You are beginning Haj (はじ). (Haj is the fifth pillar of Islam, and is a pilgrimage to Mecca during the month of Dhu al-Hijja).