After the initial flat to dress simulation (in your case from frame 0 to 35), at frame 35 go to the Modifier tab, click the drop down, and Save as Shape Key. It’s similar with @a59303’s suggestion, but instead of applying the modifier, it’s safer to just save it as a shape key. You can then go to Object Data Properties and slide the newly created shape key’s value to 1.
And after that, you can do two thing: 1) drag the walk cycle animation sequence so that it starts at frame 0, or 2) you can keep the animation that way, but you set both the start playback range to frame 35 and go to your skirt’s Physics Properties, under Cache, set the Simulation Start to frame 35 as well.
I just created the same thing, a walk cycle + cloth simulation, and you might want to see my post here.