What do you mean "without using a built in function"?
string[0].toInt gives you the ASCII value of the character because the fun get(index: Int) on String has a return type of Char, and a Char behaves closer to a Number than a String. "0".toInt() == 0 will yield true, but '0'.toInt() == 0 will yield false. The difference being the first one is a string and the second is a character.
A oneliner
string.split("").filterNot { it.isBlank() }.map { it.toInt() }
Explanation: split("") will take the string and give you a list of every character as a string, however, it will give you an empty string at the beginning, which is why we have filterNot { it.isBlank() }, we then can use map to transform every string in our list to Int
If you want something less functional and more imperative that doesn't make use of functions to convert there is this
val ints = mutableListOf<Int>() //make a list to store the values in
for (c: Char in "1234") { //go through all of the characters in the string
val numericValue = c - '0' //subtract the character '0' from the character we are looking at
ints.add(numericValue) //add the Int to the list
}
The reason why c - '0' works is because the ASCII values for the digits are all in numerical order starting with 0, and when we subtract one character from another, we get the difference between their ASCII values.
This will give you some funky results if you give it a string that doesn't have only digits in it, but it will not throw any exceptions.