Jainism is one of the oldest religions and I believe it meets your requirments of no purported revelation, enlightenment from a supernatural origin, or mystical connection with a supernatural world.
"According to Jains, souls are intrinsically pure and possess the qualities of infinite knowledge, infinite perception, infinite bliss and infinite energy. [ 28 ] In contemporary experience, however, these qualities are found to be defiled and obstructed, on account of the soul's association with a substance called karma over an eternity of beginningless time"
As soon as the concept of soul is introduced, there is a mystical connection with a supernatural world.