Theism, Charvaka and Samkhya represented Atheism.
Samkhya begins with the statement that ” God’s existence is not proved”. It
only talks about two principles, Purusha and Prakriti. Prakriti is the main
cause, Pradhanam Prakritim Prahuh ! One of the best books on Samkya is the
Samkhya Karika.
Charvaka is absolute materialism. It exhorts all to eat drink and be merry.
It is not bothered about After Life, Transmigration et al. One of the best
books on the subject is the Barhaspatya Sutras.
The Theism of Yoga and Tantra is counterbalanced by its dialectical
opposite, the Atheism of Charvaka and Samkhya.
So Indian Philosophy is Dialectical Integralism, which includes the Thesis
of Theism and the Anti Thesis of Atheism.
Both the dialectical poles are integrated in a supreme synthesis, Advaitha
Vedanta Sastra, which maintains that all this is a projection of the
Universal Mind and only the Absolute Self exists, Maya matram idam dwaitham
/ Advaitham Parmarthatha. With God or without God ( as in Buddhism ), Self
Actualisation is possible !