I've met a lot of people through our neighborhood, and through my children and their school. I've even met a few people just by seeing them out walking their dogs in the park routinely. Most of these people are just acquaintances, but some have become friends. I don't know how to answer your question as to how long it took because I can't remember precisely at what point they changed from being acquaintances to friends.
My next door neighbors are lovely people. We have little in common but I met them before we even moved in and warmed to them right away. They've always been kind to me, and gone out of their way to greet me and ask how things were going. Sometimes the quick chat I had with one of them over the back fence was the only adult contact I had in a day!
I remember feeling lonely and left out for a while at the school gates, and then I was able to overcome my shyness and found a few mothers who wanted to be friends. By the end of the first year, a new mother turned up at the school gates and was ignored and excluded as I had been when I arrived. I approached her and invited her and her daughter over to my house. She has become one of my best friends here.
When new people moved into the house over the road, I made them some muffins and went over to introduce myself. I also gave them one of my Dominos coupons to order a pizza and we've been friends ever since! Sometimes the best way to make friends is to look for other people who need friends.
I live in a small town, and small towns can be insular and provincial and perhaps harder places to make friends. On the other hand, in a small town I tend to keep coming across the same people everywhere so maybe that's made it easier to make friends. If I had waited for other American friends or international friends, or people who really understood and could relate to my situation, then I would still be waiting. Those are thin on the ground in my neighborhood. It's a good thing I can talk to them online!