```python
from typing import List, Tuple

def driest_window(rain: List[int], width: int) -> int:
    if not isinstance(rain, list) or not all(isinstance(day, int) for day in rain):
        raise ValueError("Rain must be a list of non-negative integers.")
    if not isinstance(width, int) or width <= 0 or width > len(rain):
        raise ValueError("Width must be a positive integer not larger than the number of days.")
    
    if width == len(rain):
        return 0
    
    min_sum = float('inf')
    min_start = 0
    
    for i in range(len(rain) - width + 1):
        day_sum = sum(rain[i:i+width])
        if day_sum < min_sum:
            min_sum = day_sum
            min_start = i
    
    return min_start
```