Shortest Route. 2 options
1) Little Wenatche trailhead 3000 feet and a lot of miles via the southern approach.
1a) Sauk River approach, I belive the road was fixed, but could be wrong. If so take bikes for the washed out road and hike into Glacier via White pass instead of Little Wenatche. Trade miles for elevation. Same route, south ridge Glacier Peak.
2) Take bikes. Take old road up to old trail head and hoof up the west side in 2 days. Better be in shape as its a good 9500 feet elevation gain. =)
Erm Longer options: Park at Chiwawa river trail head, hike over buck creek pass, descend open forest or find the ancient trail that used to exist(GL), cross the head of the suittle river, hike up easy open forest slopes to the Chocolate glacier, summit and return. Could do the chocolate glacier route via 1) and 1a) where one traverses Glacier peak and its??? mind blank ??? glacier on its SE
Either way, its hecka long.
If no snow on trails, super runners do glacier in a day even with the extended mileage.