Pour marinara into bottom of a baking dish (an 8 x 8 or small casserole or gratin dish).
Trim the ends off the eggplant, zucchini, and yellow squash. As carefully as you can, trim the ends off the red pepper and remove the core, leaving the edges intact, like a tube. Using a mandoline or an adjustable-blade slicer, cut the eggplant, zucchini, yellow squash, and red pepper into very thin slices, approximately 1/16-inch thick.
On top of the marinara sauce, arrange alternating slices. You may have a few extra slices. Drizzle the olive oil over the vegetables and season them generously with salt and pepper. Pull the thyme leaves off the stem and scatter them over the dish.
Cover with a piece of parchment paper that is cut to fit inside a baking dish. This ensures all veggies will be cooked to perfection and allows extra moisture to evaporate. Just covering in foil will not work as it will create too much steam and liquid.
Bake for approximately 45 to 55 minutes, until vegetables have released their liquid and are clearly cooked, but with some structure left so they are not totally limp. They should not be brown at the edges and you should see that the tomato sauce is bubbling up around them.