I was first taught to count starting from the index finger as well:
fist = 0
index = 1
index, middle = 2
index, middle, ring = 3
index, middle, ring, pinky = 4
index, middle, ring, pinky, thumb = 5
thumb = 6
thumb, index = 7
thumb, index, middle = 8
thumb, index, middle, ring = 9
(I am from Thailand, but I think this is how counting is taught in America as well?)
I thought this was universal until I went to Singapore. I was quite intrigued that in Singapore a "thumb" is not considered a number but rather a signal for "good" and instead they used thumb + pinky for 6. (The rest seems to be the same.)
Not sure why I brought that up, but I guess I had not realized that there was a difference in even the way we counted all around the world until that point.
EDIT: Formatting