```python
from typing import List, Optional

def driest_window(rain: List[int], width: int) -> Optional[int]:
    if not isinstance(rain, list):
        raise ValueError("Input is not a list.")
    if not all(isinstance(x, int) for x in rain):
        raise ValueError("All elements in the list must be integers.")
    if not all(x >= 0 for x in rain):
        raise ValueError("All elements in the list must be non-negative.")
    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.")

    if width == len(rain):
        return 0

    min_sum = float('inf')
    min_start = None

    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_start = i

    return min_start
```