Write a function that takes in a string of lowercase English-alphabet letters and returns the index of the string's first non-repeating character.

The first non-repeating character is the first character in a string that occurs only once.

If the input string doesn't have any non-repeating characters, your function should return -1.

Sample Input
string = "abcdcaf"

Sample Output
1 // The first non-repeating character is "b" and is found at index 1.