```python
def driest_window(rain: list, width: int) -> int:
    """
    Find the starting index of the width-day stretch with the smallest sum of rainfall readings.
    If multiple stretches have the same smallest sum, return the earliest start index.
    """
    if not isinstance(rain, list):
        raise ValueError("rain must be a list.")
    if not all(isinstance(x, int) for x in rain):
        raise ValueError("All readings must be integers.")
    if any(x < 0 for x in rain):
        raise ValueError("No negative readings allowed.")
    if not isinstance(width, int) or width <= 0:
        raise ValueError("Width must be a positive whole number.")
    if width > len(rain):
        raise ValueError("Width cannot be larger than the number of days.")

    min_sum = float('inf')
    min_index = 0

    for i in range(len(rain) - width + 1):
        current_sum = sum(rain[i:i+width])
        if current_sum < min_sum:
            min_sum = current_sum
            min_index = i

    return min_index
```