I'm not actually sure! I got my first pic from Tutu, she mailed it to me after visiting my house, and then Bob gave me his after giving a present to Cheri.
Not long at all, Whitney gave me tons of pics back when I had her! Fauna has also given me a lot of pics (three in four days, insane) in my second town. I've been very lucky with villagers' pics in general. Only need O'Hare's in my main town!
When Willow said she wanted to move out, I was kind've surprised but I said sure. Then I got a letter from her wit ha present. I'd never gotten a picture in a present before which made me feel really weird. I never viewed her as a best friend, I talked to her sometimes but not always. It was such a surprise!
She was also one of my first villagers and it was pretty early, maybe a month before she moved.
I haven't gotten any in ACNL (my town is only about a month old) but my first ever was Melba in Wild World. I didn't even know pictures were a thing back then and I didn't make an effort to get it from her. I must have just been playing a lot, lol
I think 3-4 months or so for my first. Marshal gave me his after I got a petition signed for him.
Beau gave me my second picture, and it was only after a week or two of having him for giving him a piece of foreign perfect fruit.
I've also gotten a couple via letters from those who have moved, but that was only after Marshal had given me his.