Use a plastic kiddie pool for this. Fill up the pool with a hose, and add dirt as you go. Swirl it up, and your doggo has the mud bath they’ve been dreaming of, even if the rain has been sparse and drought plagues your area.
When it rains, the world comes to life with new smells and sights. Everything grows muddy around you, and your dog will like splashing, watching animals, and sniffing the wet earth during a shower. Be sure it’s safe; no thunder and lightning should be in or around your neighborhood or city street.