Seattle's drinking water doesn't come from glaciers. The entirety of the Cedar River Watershed and the South Fork Tolt River Watershed are below 5500 feet. There's no glaciers there. Most of their area is below 4,000 feet. They typically have completed melting out by late May or early June, and the remaining inflows are from percolation through the ground.

These supplies last through the summer primarily based on storage behind a couple small dams on the upper reaches of Cedar and South Fork Tolt Rivers.

Seattle has had great success with conservation efforts delaying the point when demand from the growing population exceeds that supply. I think it's been pushed back literal decades, if I remember right. Climate change may accelerate it slightly again because the spring snowpack is effectively additional storage.

Regardless, whenever it happens, the response will be to raise the dams on either or both of those lakes to increase the storage capacity.