Is it the soul that must surrender to the Cosmic Self?

Yes. Each human being has an individual soul. This soul has to surrender to the Self — the Self which, in Indian terms, is called Paramatman, and is unmanifest. This Self does not take human incarnation or enter into creation, whereas the soul takes a human body and accepts limitation, imperfection and ignorance. This individual soul, which takes a human body, is not all-pervading, omniscient or omnipotent. The Self is. The soul, in its upward evolution, can some day merge into the Self and become as powerful as the Self.