Model the problem as a graph where each cell is a node, and edges exist between adjacent cells with a weight of 1 (time to move). The "distance" to a node is the earliest arrival time at that cell.

Use a priority queue (min-heap) to always expand the cell with the smallest current arrival time. For each neighbor, calculate the new arrival time as `max(current_time + 1, grid[neighbor_i][neighbor_j])`. If this new time is better than the previously recorded time for the neighbor, update it and push the neighbor into the queue.

If the bottom-right cell is reached, return the arrival time. If the queue is exhausted without reaching the cell, return -1. To optimize, skip processing a cell if the current time is already worse than the recorded time for that cell.