Siona’s excellent report (6/19/2020) has all the primary data you need, and I won’t necessarily repeat it. Following are some supplements and elaborations.
The Goat Creek Trail (#959) was the recommended route to Goat Peak in Spring and Manning’s classic 1992 book. It’s much more civilized than trail #968C from Hell’s Crossing Campground.
Trailhead is at roughly milepost 6 on the Bumping River road, on the north side.
The creek at about 4800’ is still running rather weakly (probably will dry up sometime in July).
While there are a few somewhat-masked views earlier (notably toward Nelson Ridge at around 4200’), the most open views on the Goat Creek Trail are just before the intersection with American Ridge Trail (#958) at about 5700’. The junction is marked only by an ancient wooden “American Ridge” sign nailed to a tree – turn right here. At about 5900’ are grand views of Rainier and the Fifes Peaks. In case the party is totally pooped at this point, you’ve now seen all the cherries on top of the Goat Peak Sundae.
I noticed mosquitoes investigating my hand after stopping for a minute or so twice on the way up, but otherwise wasn’t particularly aware of bugs until around the summit. Even there they weren’t very aggressive.
Most of the trail is good for social distancing (i.e., you can easily get off the trail, or, in the few stretches where cut into steepish slopes, you can see people a ways away and often find a good spot). The last half-mile or so is a bit more problematic (mostly on a steep slope, but there is sometimes a bit of space on switchbacks or elsewhere).
There was no one else on the trail all day (except at Goat Peak summit – they came up one of the other routes).

Comments
Seattle_Wayne on Goat Creek, American Ridge, Goat Peak
Awesome trip report. I experienced the same. Thank you.
Posted by:
Seattle_Wayne on Jun 26, 2020 11:59 AM