Reversing / enriching typeclass resolution in haskell

Question

Is there any trick to get the "ancestor" proof of a typeclass instance ?

data Dict c = c => Dict

newtype Prod a b = MkProd {getProd :: (a, b)}

class Mk a where mk :: a

instance (Mk a, Mk b) => Mk (Prod a b) where
  mk = MkProd (mk, mk)

challenge :: Mk (Prod a b) => Dict (Mk b)
challenge = Dict

-- Could not deduce (Mk b) arising from a use of ‘Dict’
-- from the context: Mk (Prod a b)

Attempting with "UndecidableInstances" yields an overlap error

newtype Prod a b = MkProd {getProd :: (a, b)}

class Make a where make :: a

instance {-# OVERLAPPING #-} (Make a, Make b) => Make (Prod a b) where
  make = MkProd (make, make)

instance {-# OVERLAPPABLE #-} (Make (Prod a b)) => Make a where
  make = let (MkProd (a, b)) = make @(Prod a b) in a

challenge :: Make (Prod a b) => Dict (Make a)
challenge = Dict -- • Overlapping instances for Make a arising from a use of ‘Dict’