Find index with positive suffix sums

Given an unsorted integer array $A$, find an index $i$ such that every cumulative sum starting from $i$ to the end of the array is strictly positive:

• $A[i] > 0$
• $A[i] + A[i+1] > 0$
• $A[i] + A[i+1] + A[i+2] > 0$
• ...
• $\sum_{k=i}^{n-1} A[k] > 0$

Return any valid index. If no such index exists, return $-1$.

First describe a baseline solution, then optimize it. Aim for better than $O(n^2)$ time.