Hello Dan. It is wonderful that you are cooking from scratch, and this is a very common issue when baking raw ingredients together in a single dish.
The main reason your vegetables turn to mush before the poultry finishes is due to heat distribution, moisture retention, and ingredient density. To achieve an even bake where everything finishes at the exact same time, you can follow this standard layering method.
First, place your hard, dense root vegetables (such as diced potatoes, carrots, parsnips, and celery) across the bottom of the dish. The bottom receives the most direct conductive heat from the oven rack, and these sturdy vegetables require the longest cooking time in liquid to become tender.
Second, arrange your chicken directly over the dense vegetables. Make sure your chicken is cut into uniform, bite-sized pieces so that every piece cooks at the same rate. Searing the chicken pieces in a pan for two to three minutes beforehand is optional, but it gives the meat a helpful head start and adds great flavor.
Third, pour your seasoned liquid, stock, or sauce evenly over the top. The liquid will settle among the bottom vegetables and surround the meat, allowing the steam and simmering liquid to cook the chicken safely and gently without drying it out.
Fourth, if you are using delicate vegetables (such as peas, bell peppers, or mushrooms) or toppings like breadcrumbs and cheese, keep them out of the dish initially. Cover the casserole tightly with foil and bake at 375 degrees Fahrenheit (190 degrees Celsius) until the chicken reaches an internal temperature of 165 degrees Fahrenheit. During the final 15 minutes of baking, remove the foil and add your delicate vegetables and crunchy toppings so they retain their texture and color.
Following this order will ensure your chicken is thoroughly cooked and juicy while your vegetables maintain the right balance of tenderness.