Mount Stuart has many routes to the top. One of the most popular non-technical routes is Cascadian Couloir. It is a southern route that is mostly a class 2/3 scramble. Its a really nice introduction to scrambling for people who want a bit more of an adventure compared to standard hiking.
To approach the Cascadian Couloir route from Seattle, drive east on I-90 towards Cle Elum. You'll want to park at the Esmeralda Trailhead. Sometimes also referred to as the Ingalls Lake Trailhead as it will take you to Lake Ingalls, a beautiful day hike.
The trail starts out flat but quickly starts to switchback. At about 1.45 miles and 1,000 feet of elevation gain, you'll reach a fork in the trail. The left fork will take you to Lake Ingalls, and the right fork will take you to Longs Pass. You have 2 options at this point.
If you plan to camp 1 night at the base of Mount Stuart, which is what we did, I would recommend taking the scenic route towards Ingalls Pass and Lake Ingalls. You can jump in the lake, and/or take a few pictures of the nice view of Mount Stuart from Lake Ingalls. Otherwise, you can take the right fork and head straight towards the base of Mount Stuart.
This route is definitely possible in 1 day. However, the entire journey would span roughly 5.5 miles and 6500 feet of elevation gain. It's a long day with potentially slow moving during the scramble but, definitely doable.
Before we went to sleep, we took one last look at the objective
We left camp at around 5:00am and we had spectacular weather, and views while the sun rose and we made our way up the couloir. The initial part of the couloir is pretty chossy with a lot of loose rock. There is a distinct trail you follow but, it's not always clear which way to go is the best. For most of the morning you are in the shade since the couloir is south facing.
The route turns into more of a proper scramble the higher you get. In addition to that, the views get better the higher you get as well. We got a nice view of Mount Rainier the during the entire ascent.
After around 2-3,000 feet of elevation gain, you'll reach a point where it's truly a scramble and there isn't a dirt trail to follow. The scrambling is really fun. The rock all feels very solid but, I'd still definitely recommend a helmet. I don't remember seeing many cairns along the way but, it's not very difficult to read the route. Once you get to the top of the couloir, you pretty much traverse climbers left towards the peak. There is a bit of exposure in places but, I don't think a rope is necessary. It will most likely just slow you down and create unnecessary complications.
We really lucked out with great weather and views. The summit is very craggy and has a lot of different points to take in the view. We spent a good amount of time on the summit before heading back down. After the long descent we made our way back to the lake and jump in for a nice alpine lake cool down.